@incollection{BHS2020,

AUTHOR = {Behrndt, J. and Hassi, S. and de Snoo, H.}, BOOKTITLE = {Monographs in Mathematics}, VOLUME = {108}, TITLE = {Boundary Value Problems, Weyl Functions, and Differential Operators}, PUBLISHER = {Birkh{\"a}user}, YEAR = {2020}

}

@article{BroerHanssmann2020, title = "A Galilean dance 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons", journal = "Discrete & Continuous Dynamical Systems - S", volume = "13", number = "1937-1632_2020_4_1043", pages = "1043", year = "2020", note = "", issn = "1937-1632", doi = "10.3934/dcdss.2020062", url = "http://aimsciences.org//article/id/9c6d0761-a61f-484e-803d-6abdf1112376", author= {Broer, H. W. and Han{\ss}mann, H.}, keywords = "Dimension theory","Poincaré recurrences","multifractal analysis", }

@Article{EndoValesin2020, author = {Endo, E. O. and Valesin, D.}, title = {Local limits of spatial Gibbs random graphs}, journal="ALEA, Lat. Am. J. Probab. Math. Stat.", year="2020", volume="17", pages="51--63", abstract="We study the spatial Gibbs random graphs introduced in Mourrat andValesin (2018) from the point of view of local convergence. These are randomgraphs embedded in an ambient space consisting of a line segment, defined througha probability measure that favors graphs of small (graph-theoretic) diameter butpenalizes the presence of edges whose extremities are distant in the geometry of theambient space. In Mourrat and Valesin (2018) these graphs were shown to exhibitthreshold behavior with respect to the various parameters that define them; thisbehavior was related to the formation of hierarchical structures of edges organizedso as to produce a small diameter. Here we prove that, for certain values of theunderlying parameters, the spatial Gibbs graphs may or may not converge locally,in a manner that is compatible with the aforementioned hierarchical structures.", doi="10.30757/ALEA.v17-03", url="https://doi.org/10.30757/ALEA.v17-03", }

@Article{vanEnterMiekisz2020, author= {A.C.D. van Enter and J. Miȩkisz}, title="Typical Ground States for Large Sets of Interactions", journal="J. Stat. Phys.", year="2020", volume="181", pages="1906–1914", doi = "10.1007/s10955-020-02647-4", url = "https://doi.org/10.1007/s10955-020-02647-4", abstract="We discuss what ground states for generic interactions look like. We note that a recent result, due to Morris, implies that the behaviour of ground-state measures for generic interactions is similar to that of generic measures. In particular, it follows from his observation that they have singular spectrum and that they are weak mixing, but not mixing.", }

@Article{vanEnterKoivusaloMiekisz2020, author= {A.C.D. van Enter, H. Koivusalo and J. Miȩkisz}, title="Sturmian Ground States in Classical Lattice–Gas Models", journal="J. Stat. Phys.", year="2020", volume="178", pages="832--844", abstract="We construct for the first time examples of non-frustrated, two-body, infinite-range, one-dimensional classical lattice–gas models without periodic ground-state configurations. Ground-state configurations of our models are Sturmian sequences defined by irrational rotations on the circle. We present minimal sets of forbidden patterns which define Sturmian sequences in a unique way. Our interactions assign positive energies to forbidden patterns and are equal to zero otherwise. We illustrate our construction by the well-known example of the Fibonacci sequences.", doi="10.1007/s10955-019-02464-4", url="https://doi.org/10.1007/s10955-019-02464-4", }

@article{GaoEfstathiou2020, Title = {Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies}, Author = {Gao, Jian and Efstathiou, Konstantinos}, Journal = {Phys. Rev. E}, Doi = {10.1103/PhysRevE.101.022302}, Issue = {2}, Month = {Feb}, Numpages = {6}, Pages = {022302}, Volume = {101}, Year = {2020} }

@Article{JungWaalkens2019, author={Jung, C. and Waalkens, H.}, title="Dynamics associated with the normally hyperbolic invariant manifold that governs the ionization of hydrogen in a circularly polarized electric field", journal="Int. J. Bif. Chaos", number= {8}, volume = {30}, pages = {2030022}, year="2020", doi = {https://doi.org/10.1142/S0218127420300220}, }

@ARTICLE{MBE2020,

Author = {Martynchuk, N. and Broer, H.W. and Efstathiou, K.}, Title = {{H}amiltonian monodromy and {M}orse theory}, Journal = {Comm. Math. Phys.}, Abstract = {We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takens's index theorem, which specifies how the energy-h Chern number changes when h passes a non-degenerate critical value, and a choice of admissible cycles in Fomenko-Zieschang theory. Connections of our result to some of the existing approaches to monodromy are discussed.}, Doi = {10.1007/s00220-019-03578-2}, Number = {2}, Pages = {1373-1392}, Volume = {375}, Year = {2020}

}

@Article{SzaboValesin2020, author= {Szabó, R. and Valesin, D.}, title="Inhomogeneous Percolation on Ladder Graphs", journal="Journal of Theoretical Probability", year="2020", volume="33", pages="992--1010", doi="10.1007/s10959-019-00896-y", url="https://doi.org/10.1007/s10959-019-00896-y", }

%

2019

@Article{Arzhakova2019, author = {Arzhakova, E. and Verbitskiy, E.}, title = {Tropical Limits of Decimated Polynomials}, journal="Arnold Mathematical Journal", year="2019", month="Mar", day="01", volume="5", number="1", pages="57--67", abstract="Motivated by some problems that originate in Statistical Physics and Algebraic Dynamics, we discuss a particular renormalization mechanism of multivariate Laurent polynomials which is called a decimation, and the corresponding tropical limiting shape result obtained in Arzhakova et al. (Decimation of principal actions. Preprint, 2018).", issn="2199-6806", doi="10.1007/s40598-019-00108-9", url="https://doi.org/10.1007/s40598-019-00108-9", }

@ARTICLE{BarNatanVDVeen2019,

Author = {Bar-Natan, D. and van der Veen, R.}, Title = {A polynomial time knot polynomial}, Journal = {Proc. Amer. Math. Soc.}, Abstract = {We present the strongest known knot invariant that can be computed effectively (in polynomial time).}, Doi = {10.1090/proc/14166}, Pages = {377--397}, Volume = {147}, Year = {2019}

}

@article{berghout_fernández_verbitskiy_2019, title={On the relation between Gibbs and $g$ -measures}, volume={39}, DOI={10.1017/etds.2018.13}, number={12}, journal={Ergodic Theory and Dynamical Systems}, publisher={Cambridge University Press}, author={Berghout, S. and Fernand{\'e}z, R. and Verbitskiy, E.}, year={2019}, pages={3224–3249}, }

@incollection{BEEKNR2019,

author = {R. Bissacot and E. Endo and A.C.D. van Enter and B. Kimura and A. Le Ny and W.M. Ruszel}, title = {Dyson Models Under Renormalization and in Weak Fields}, booktitle = {Sojourns in Probability Theory and Statistical Physics - I}, publisher = {Springer}, year = 2019, editor = {Sidoravicius, V.}, pages = {123--127}, address = {Springer}, note = {Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman}

}

@Article{BroerHanssmann2019, author= {Broer, H. W. and Han{\ss}mann, H.}, title="Bifurcations in Volume-Preserving Systems", journal="Acta Applicandae Mathematicae", year="2019", month="Aug", day="01", volume="162", number="1", pages="3--32", abstract="We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from `generic' bifurcations of structure-less `dissipative' vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.", issn="1572-9036", doi="10.1007/s10440-019-00254-4", url="https://doi.org/10.1007/s10440-019-00254-4", }

@Misc{BroerDeSnoo2019,

title = {Wiskundigen in Groningen}, author = { Broer, H.W. and de Snoo, H.S.V. }, year = {2019},

HOWPUBLISHED = { Nieuw Archief voor Wiskunde 5/20:277--279 }, }

@Misc{Broer2019,

title = {J.Ch. Boland: een Groningse wiskundige uit Amsterdam}, author = { Broer, H.W. }, year = {2019},

HOWPUBLISHED = { Nieuw Archief voor Wiskunde 5/20:2280--282 }, }

@ARTICLE{CDEW2018,

author = {Chiscop, I. and Dullin, H. R. and Efstathiou, K. and Waalkens, H.}, title = {A Lagrangian Fibration of the Isotropic 3-Dimensional Harmonic Oscillator with Monodromy},

volume = {60}, number = {3}, pages = {032103}, year = {2019}, doi = {10.1063/1.5053887}, URL = {https://aip.scitation.org/doi/abs/10.1063/1.5053887},

```
journal = {J. Math. Phys.},
year = {2019},
abstract = {The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three Poisson commuting integrals and, correspondingly, three commuting operators, one of which is the Hamiltonian. We show that the Lagrangian fibration defined by the Hamiltonian, the $z$ component of the angular momentum, and a quartic integral obtained from separation in prolate spheroidal coordinates
```

has a non-degenerate focus-focus point, and hence non-trivial Hamiltonian monodromy for sufficiently large energies. The joint spectrum defined by the corresponding commuting quantum operators has non-trivial quantum monodromy implying that one cannot globally assign quantum numbers to the joint spectrum. }, }

@article{DyerVegterWintraecken2019, author = {Dyer, R. and Vegter, G. and Wintraecken, M.H.M.J.}, journal = {Journal of Computational Geometry}, number = {1}, pages = {223--256}, title = {{Simplices modelled on spaces of constant curvature}}, volume = {10}, doi={10.20382/jocg.v10i1a9}, url = {https://doi.org/10.20382/jocg.v10i1a9}, year = {2019} }

@inproceedings{Ebbens2019, author = {Ebbens, Y.M. and Iordanov, I. and Teillaud, M. and Vegter, G.}, booktitle = {Abstracts of the 34th European Workshop on Computational Geometry}, keywords = {EbbensIordanovTeillaudVegter2019}, title = {{Delaunay triangulations of symmetric hyperbolic surfaces}}, url = {http://www.eurocg2019.uu.nl/papers/15.pdf}, year = {2019} }

@INPROCEEDINGS{Enter2019,

AUTHOR = {Aernout C. D. van Enter}, TITLE = {One-Sided Versus Two-Sided Stochastic Descriptions}, BOOKTITLE = {Springer Proceedings in Mathematics & Statistics}, YEAR = {2019}, PAGES = {21--33}, PUBLISHER = {Springer}, EDITOR = {Gayrard, V. and Arguin, L.-P. and Kistler and N., Kourkova, I.}

}

@article{EKRS2019, title = {Nucleation for One-Dimensional Long-Range Ising Models}, journal = "J. Stat. Phys.", volume = {174}, year = "2019", pages = {1327--1345}, author = "A.C.D. van Enter and B. Kimura and W. Ruszel and C. Spitoni ", }

@article{Feldbrugge2019, abstract = {The topology and geometry of random fields—in terms of the Euler characteristic and the Minkowski functionals—has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial non-Gaussianities would form a valuable clue on the physics of the early Universe. The virtue of both the Euler characteristic and the Minkowski functionals in general, lies in the fact that there exist closed form expressions for their expectation values for Gaussian random fields. However, the Euler characteristic and Minkowski functionals are summarizing characteristics of topology and geometry. Considerably more topological information is contained in the homology of the random field, as it completely describes the creation, merging and disappearance of topological features in superlevel set filtrations. In the present study we extend the topological analysis of the superlevel set filtrations of two-dimensional Gaussian random fields by analysing the statistical properties of the Betti numbers—counting the number of connected components and loops—and the persistence diagrams—describing the creation and mergers of homological features. Using the link between homology and the critical points of a function—as illustrated by the Morse-Smale complex—we derive a one-parameter fitting formula for the expectation value of the Betti numbers and forward this formalism to the persistence diagrams. We, moreover, numerically demonstrate the sensitivity of the Betti numbers and persistence diagrams to the presence of non-Gaussianities.}, author = {Feldbrugge, J. and van Engelen, M. and van de Weygaert, R. and Pranav, P. and Vegter, G.}, doi = {10.1088/1475-7516/2019/09/052}, issn = {1475-7516}, journal = {Journal of Cosmology and Astroparticle Physics}, number = {09}, pages = {52}, publisher = {IOP Publishing}, title = {{Stochastic homology of Gaussian vs. non-Gaussian random fields: graphs towards Betti numbers and persistence diagrams}}, url = {http://dx.doi.org/10.1088/1475-7516/2019/09/052}, volume = {2019}, year = {2019} }

@article{GBS:2019b,

author = {Gaiko, V.A. and Broer, H.W. and Sterk, A.E.}, title = {Global bifurcation analysis of {Topp} system}, journal = {Cybernetics and Physics}, volume = {8}, issue = {4}, year = {2019}, pages = {244-250}, url = {http://lib.physcon.ru/doc?id=58b610906267}

}

@article{HassiSandoviciDeSnoo2019, title = {Factorized sectorial relations, their maximal sectorial extensions, and form sums}, journal = "Banach J. Math. Anal.", volume = {to appear}, year = "2019", author = "S. Hassi and A. Sandovici and H.S.V. de Snoo", }

@article{HoveijnWaalkensZaman2019, title = "Critical points of the integral map of the charged three-body problem", journal = "Indagationes Mathematicae", volume = "30", number = "1", pages = {165--196}, year = "2019", issn = "0019-3577", doi = "10.1016/j.indag.2018.09.006", url = "http://www.sciencedirect.com/science/article/pii/S0019357718303495", author = "I. Hoveijn and H. Waalkens and M. Zaman", keywords = "Charged three-body problem, Integral manifold, Critical point, Relative equilibrium, Central configuration", abstract = "This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of the map of integrals. Due to the non-compactness of the integral manifolds one has to take into account besides ‚Äòordinary‚Äô critical points also critical points at infinity. In the present paper we concentrate on ‚Äòordinary‚Äô critical points and in particular elucidate their connection to central configurations. In a second paper we will study critical points at infinity. The implications for the Hill regions, i.e. the projections of the integral manifolds to configuration space, are the subject of a third paper." }

@article{JSG:2019,

author = {De Jong, T.G. and Sterk, A.E. and Guo, F.}, title = {Numerical method to compute hypha tip growth for data driven validation}, journal = {IEEE Access}, volume = {7}, year = {2019}, pages = {53766-53776}, doi = {http://dx.doi.org/10.1109/ACCESS.2019.2912638},

}

@article{KS:2019,

author = {Van Kekem, D.L. and Sterk, A.E.}, title = {Symmetries in the {L}orenz-96 model}, journal = {International Journal of Bifurcation and Chaos}, volume = {29}, year = {2019}, pages = {1950008}, section = {articles}, topic = {dynsys}, url = {http://dx.doi.org/10.1142/S0218127419500081}

}

@ARTICLE{KrajnakWaalkens2019,

AUTHOR = {Krajňák, V. and Waalkens, H.}, TITLE = {Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction}, JOURNAL = {J. Math. Chem.}, VOLUME = {to appear}, YEAR = {2019}, doi = {10.1007/s10910-019-01083-4}, url = {https://doi.org/10.1007/s10910-019-01083-4},

}

@article{doi:10.1002/rsa.20805, author = {de Lima, Bernardo N. B. and Rolla, Leonardo T. and Valesin, Daniel}, title = {Monotonicity and phase diagram for multirange percolation on oriented trees}, journal = {Random Structures \& Algorithms}, volume = {55}, number = {1}, pages = {160-172}, keywords = {critical curve, long range percolation, monotonicity of connectivity}, doi = {10.1002/rsa.20805}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20805}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.20805}, abstract = {We consider Bernoulli bond percolation on oriented regular trees, where besides the usual short bonds, all bonds of a certain length are added. Independently, short bonds are open with probability p and long bonds are open with probability q. We study properties of the critical curve which delimits the set of pairs (p,q) for which there are almost surely no infinite paths. We also show that this curve decreases with respect to the length of the long bonds.}, year = {2019} }

@ARTICLE{MDEW2019,

author = {Martynchuk, N. and Dullin, H.R. and Efstathiou, K. and Waalkens, H.}, title = {Scattering invariants in Euler's two-center problem}, journal = {Nonlinearity}, year = {2019}, volume = {32}, number = {4}, pages = {1296--1326}, doi = {10.1088/1361-6544/aaf542}, url = {https://doi.org/10.1088%2F1361-6544%2Faaf542}, abstract = {The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positive and negative) strengths of the centers. Combining techniques from scattering theory and Liouville integrability, we show that this spatial problem has topologically non-trivial scattering dynamics, which we identify as scattering monodromy. The approach that we introduce in this paper applies more generally to scattering systems that are integrable in the Liouville sense.},

}

@article{MOUNTFORD20192783, title = "The asymmetric multitype contact process", journal = "Stochastic Processes and their Applications", volume = "129", number = "8", pages = "2783 - 2820", year = "2019", issn = "0304-4149", doi = "10.1016/j.spa.2018.08.006", url = "http://www.sciencedirect.com/science/article/pii/S0304414918304113", author = "Thomas Mountford and Pedro Luis Barrios Pantoja and Daniel Valesin", abstract = "We study the multitype contact process on Zd under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, the stronger type has a positive probability of never going extinct. Conditionally on this event, it takes over a ball of radius growing linearly in time. We also completely characterize the set of stationary distributions of the process and prove a complete convergence theorem." }

@article{Pranav2019, author = {Pranav, P. and Van De Weygaert, R. and Vegter, G. and Jones, B. J. T. and Adler, R. J. and Feldbrugge, J. and Park, C. and Buchert, T. and Kerber, M.}, doi = {10.1093/mnras/stz541}, issn = {13652966}, journal = {Monthly Notices of the Royal Astronomical Society}, keywords = {Cosmic background radiation,Cosmology: theory,Large-scale structure of universe,Methods: data analysis,Methods: numerical,Methods: statistical}, number = {3}, pages = {4167--4208}, publisher = {Oxford University Press}, title = {{Topology and geometry of Gaussian random fields I: On Betti numbers, Euler characteristic, and Minkowski functionals}}, volume = {485}, year = {2019} }

@article{prandi2019, author = {Prandi, D. and Rizzi, L. and Seri, M.}, doi = "10.4310/jdg/1549422105", fjournal = "Journal of Differential Geometry", journal = "J. Differential Geom.", month = "02", number = "2", pages = "339--379", publisher = "Lehigh University", title = "A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators", url = "https://doi.org/10.4310/jdg/1549422105", volume = "111", year = "2019", }

@Misc{Seri2019,

title = {Exploring Haskell}, author = { Seri, M. }, year = {2019}, url = {https://www.manning.com/books/exploring-haskell}, howpublished = {Manning},

}

@article{SterkWaalkensGhane2019,

author = {Sterk, A. E. and Waalkens, H. and Ghane, H.}, title = "{Chaotic dynamics from a pseudo-linear system}", year = {2019}, month = {02}, journal = {IMA Journal of Mathematical Control and Information}, abstract = "{Investigating the possibility of applying techniques from linear systems theory to the setting of non-linear systems has been the focus of many papers. The pseudo-linear (PL) form representation of non-linear dynamical systems has led to the concept of non-linear eigenvalues (NEValues) and non-linear eigenvectors (NEVectors). When the NEVectors do not depend on the state vector of the system, then the NEValues determine the global qualitative behaviour of a non-linear system throughout the state space. The aim of this paper is to use this fact to construct a non-linear dynamical system of which the trajectories of the system show continual stretching and folding. We first prove that the system is globally bounded. Next we analyse the system numerically by studying bifurcations of equilibria and periodic orbits. Chaos arises due to a period doubling cascade of periodic attractors. Chaotic attractors are presumably of H√©non-like type, which means that they are the closure of the unstable manifold of a saddle periodic orbit. We also show how PL forms can be used to control the chaotic system and to synchronize two identical chaotic systems.}", doi = {10.1093/imamci/dnz005}, url = {https://dx.doi.org/10.1093/imamci/dnz005}, eprint = {http://oup.prod.sis.lan/imamci/advance-article-pdf/doi/10.1093/imamci/dnz005/27721126/dnz005.pdf},

}

@PHDTHESIS{Szabo2019,

ADDRESS = {Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence}, ANNOTE = {Advisors: A.C.D. van Enter and D. Valesin, 61 pages}, AUTHOR = {Szabó, R.}, PAGES = {61}, SCHOOL = {University of Groningen}, TITLE = {Inhomogeneous contact process and percolation}, TYPE = {PhD Dissertation}, URL = "http://hdl.handle.net/11370/a3962a33-9d30-4714-980c-b5cc4ca56cfb", YEAR = {2019},

}

@ARTICLE{TSMWP2019,

TITLE = {Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator}, AUTHOR = {Tajik, F. and Sedighi, M. and Masoudi, A. A. and Waalkens, H. and Palasantzas, G.}, JOURNAL = {Phys. Rev. E}, VOLUME = {100}, ISSUE = {1}, PAGES = {012201}, NUMPAGES = {13}, YEAR = {2019}, MONTH = {jul}, DOI = {10.1103/PhysRevE.100.012201}, URL = {https://link.aps.org/doi/10.1103/PhysRevE.100.012201},

}

@article{VermerenBravettiSeri2019,

author={M. Vermeeren and A. Bravetti and M. Seri}, title={Contact variational integrators}, journal={Journal of Physics A: Mathematical and Theoretical}, url={http://iopscience.iop.org/10.1088/1751-8121/ab4767}, notes={DOI: 10.1088/1751-8121/ab4767}, year={2019},

}

@inproceedings{Wintraecken2019, author = {Wintraecken, M.H.M.J. and Vegter, G.}, booktitle = {Proceedings of the 31st Canadian Conference in Computational Geometry (CCCG 2019)}, file = {:Users/gert/Documents/Mendeley Desktop/Wintraecken, Vegter - 2019 - The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds.pdf:pdf}, pages = {275--279}, title = {{The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds}}, url = {https://sites.ualberta.ca/~cccg2019/#proceedings}, year = {2019} }

%

2018

@article{andjel2018, author = {Andjel, Enrique and Mountford, Thomas and Valesin, Daniel}, doi = "10.3150/17-BEJ927", fjournal = "Bernoulli", journal = "Bernoulli", month = "08", number = "3", pages = "2256--2277", publisher = "Bernoulli Society for Mathematical Statistics and Probability", title = "Equilibrium of the interface of the grass-bushes-trees process", url = "https://doi.org/10.3150/17-BEJ927", volume = "24", year = "2018" }

@Article{Bissacot2018, author={Bissacot, R. and Endo, E.O. and van Enter, A.C.D. and Kimura, B. and Ruszel, W.M.}, title="Contour Methods for Long-Range Ising Models: Weakening Nearest-Neighbor Interactions and Adding Decaying Fields", journal= "Annales Henri Poincar{\'e}", year="2018", month="Aug", day="01", volume="19", number="8", pages="2557--2574", doi="10.1007/s00023-018-0693-3", url="https://doi.org/10.1007/s00023-018-0693-3", }

@Article{BroerHansmannWagener2018, author={Broer, H.W. and Han{\ss}mann, H. and Wagener, F.}, title="Persistence Properties of Normally Hyperbolic Tori", journal= "Reg. Chaot. Dyn.", year="2018", volume="23", number="2", pages="212--225", doi="10.1134/S1560354718020065", url="https://doi.org/10.1134/S1560354718020065", }

@Article{Bissacotetal2018b, author={Bissacot, R. and Endo, E.O. and van Enter, A.C.D. and Le Ny, A.}, title="Entropic Repulsion and Lack of the g-Measure Property for Dyson Models", journal= "Commun. Math. Phys.", year="2018", volume="363", number="3", pages="767--788", doi="10.1007/s00220-018-3233-6", url="https://doi.org/10.1007/s00220-018-3233-6", }

@article{Cai2018,

Author = {Cai, X. and Efstathiou, K. and Xie, X. and Wu, Y. and Shi, Y. and Yu, L.}, Doi = {10.1111/cgf.13325}, Journal = {Computer Graphics Forum}, Title = {A Study of the Effect of Doughnut Chart Parameters on Proportion Estimation Accuracy}, Year = {2018}

}

@Article{CENR2018, author={Coquille, L. and van Enter, A.C.D. and Le Ny, A. and Ruszel, W.M. }, title="Absence of Dobrushin States for 2d Long-Range Ising Models", journal= "J. Stat. Phys.", year="2018", volume="172", number="5", pages="1210--1222", doi="10.1007/s10955-018-2097-7", url="https://doi.org/10.1007/s10955-018-2097-7", }

@Article{DCEH2018, author={Duminil-Copin, H. and van Enter, A.C.D. and Hulshof, T.}, title="Higher order corrections for anisotropic bootstrap percolation", journal= "Probab. Theory Relat. Fields", year="2018", volume="172", number="1--2", pages="191--243", doi="10.1007/s00440-017-0808-7", url="https://doi.org/10.1007/s00440-017-0808-7", }

@PHDTHESIS{Endo2018,

ADDRESS = {Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence}, ANNOTE = {Advisors: R. Bissacot, A. C. D. van Enter and D. Valesin, 106 pages}, AUTHOR = {Endo, E.O.}, PAGES = {106}, SCHOOL = {University of Groningen}, TITLE = {Gibbs measures for models on lines and trees}, TYPE = {PhD Dissertation}, URL = "http://hdl.handle.net/11370/f1a78db4-df1a-4c41-ab72-d36c700a9f67", YEAR = {2018},

}

@article{DullinWaalkens2018,

title = {Defect in the Joint Spectrum of Hydrogen due to Monodromy}, author = {Dullin, Holger R. and Waalkens, Holger}, journal = {Phys. Rev. Lett. (Editors' Suggestion)}, volume = {120}, issue = {2}, pages = {020507}, numpages = {5}, year = {2018}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.120.020507}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.020507}

}

@inproceedings{Enter:2018,

author = {Aernout C. D. van Enter}, title = {Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation}, booktitle = {Probabilistic Cellular Automata (Theory, Applications and Future Perspectives)}, year = {2018}, pages = {69--77}, publisher = {Springer}, editor = {Pierre-Yves LouisFrancesca R. Nardi}, url = {http://www.springer.com/gp/book/9783319655567#aboutAuthors},

}

@article{Gao2018,

Author = {Gao, J. and Efstathiou, K.}, Doi = {10.1103/PhysRevE.98.042201}, Journal = {Physical Review E}, Pages = {042201}, Title = {Self-consistent Method and Steady States of Second-order Oscillators}, Volume = {98}, Year = {2018},

}

@PHDTHESIS{Garst2018,

ADDRESS = {Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence}, ANNOTE = {Advisors: H. W. Broer, J. Aarts and A. Sterk, 103 pages}, AUTHOR = {Garst, S. H. P.}, PAGES = {103}, SCHOOL = {University of Groningen}, TITLE = {Dynamics amidst folding and twisting in 2-dimensional maps}, TYPE = {PhD Dissertation}, URL = "http://hdl.handle.net/11370/e99cbf70-965a-4e71-8572-f098a8c9662d", YEAR = {2018},

}

@article{HassiSnooWinkler2018, author = {S. Hassi and H.S.V. de Snoo and H. Winkler}, journal = "Operator Theory: Adv. Appl.", pages = {335--355}, title = "Limit properties of eigenvalues in spectral gaps", volume = "263", year = "2018", }

@article{HassiSebestyeenSnoo2018, author = {S. Hassi and Z. Sebestyén and H. de Snoo }, journal = "Acta Sci. Math. (Szeged)", pages = {465–-507}, title = "Lebesgue type decompositions for linear relations and Ando’s uniqueness criterion", volume = "84", year = "2018", }

@article{HassiMoellerSnoo2018, author = {Hassi, S. and M{\"o}ller, M. and de Snoo, H.}, title = "Limit-point/limit-circle classification for Hain–L{\"u}st type equations", journal = "Mathematische Nachrichten", volume = "291", number = {4}, year = {2018}, pages = {652-668}, doi = {10.1002/mana.201600254}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201600254}, }

@article{HeydenreichHirschValesin2018, author = {Heydenreich, M. and Hirsch, C. and Valesin, D.}, title = "Uniformity of hitting times of the contact process", journal = {Latin American Journal of Probability and Statistics, Alea}, volume = "15", year = {2018}, pages = {233-245}, doi = {10.30757/ALEA.v15-11}, url = {http://alea.impa.br/articles/v15/15-11.pdf}, }

@Article{Kekem2018c, author = {van Kekem, D.L. and Sterk, A.E.}, title = {Symmetries in the {L}orenz-96 model}, journal = {Int. J. Bif. Chaos}, year = {2018}, volume = "accepted", pages = {}, }

@Article{Kekem18b, author = {van Kekem, D.L. and Sterk, A.E.}, title = {Wave propagation in the {L}orenz-96 model}, journal = {Nonlinear Processes in Geophysics}, volume = {25}, number = {2}, year = {2018}, pages = {301--314}, url = {https://doi.org/10.5194/npg-25-301-2018}, doi = {10.5194/npg-25-301-2018}, }

@Article{Kekem18a, author = {Kekem, D.L. van and Sterk, A.E.}, title = {Travelling waves and their bifurcations in the {L}orenz-96 model}, year = {2018}, volume = {367}, pages = {38--60}, journal = {Physica D}, doi = {10.1016/j.physd.2017.11.008}, url = {https://doi.org/10.1016/j.physd.2017.11.008}, }

@PHDTHESIS{Kekem2018b,

ADDRESS = {Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence}, ANNOTE = {Advisors: H. W. Broer and A. Sterk, 195 pages}, AUTHOR = {van Kekem, D. L.}, PAGES = {195}, SCHOOL = {University of Groningen}, TITLE = {Dynamics of the Lorenz-96 model: Bifurcations, symmetries and waves}, TYPE = {PhD Dissertation}, URL = "http://hdl.handle.net/11370/c67926eb-c8ef-4b9a-a48a-6e965f7d2262", YEAR = {2018},

}

@Article{KrajnakWaalkens2018, author={Krajňák, V. and Waalkens, H.}, title="The phase space geometry underlying roaming reaction dynamics", journal="Journal of Mathematical Chemistry", year="2018", volume ="56", pages = "2341--2378", number = "8", abstract="Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable amount of time and extracts another hydrogen atom from the molecule prior to dissociation. This phenomenon has been coined roaming and has since been reported in the dissociation of a number of other molecules. In this paper we investigate roaming in Chesnavich's {\$}{\$}{\backslash}hbox {\{}CH{\}}{\_}4^+{\$}{\$} CH 4 + model. During dissociation the free hydrogen must pass through three phase space bottleneck for the classical motion, that can be shown to exist due to unstable periodic orbits. None of these orbits is associated with saddle points of the potential energy surface and hence related to transition states in the usual sense. We explain how the intricate phase space geometry influences the shape and intersections of invariant manifolds that form separatrices, and establish the impact of these phase space structures on residence times and rotation numbers. Ultimately we use this knowledge to attribute the roaming phenomenon to particular heteroclinic intersections.", issn="1572-8897", doi="10.1007/s10910-018-0895-4", url="https://doi.org/10.1007/s10910-018-0895-4", key = {published}; }

@PHDTHESIS{Martynchuk2018,

ADDRESS = {Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence}, ANNOTE = {Advisors: H. W. Broer and K. Efstathiou, 121 pages}, AUTHOR = {Martynchuk, N.}, PAGES = {121}, SCHOOL = {University of Groningen}, TITLE = {On monodromy in integrable Hamiltonian systems}, TYPE = {PhD Dissertation}, URL = "http://hdl.handle.net/11370/238a4814-3ea1-4ca6-8b9a-493a8b3c09b4", YEAR = {2018},

}

@article{mourrat2018, author = {Mourrat, Jean-Christophe and Valesin, Daniel}, doi = "10.1214/17-AAP1316", fjournal = "The Annals of Applied Probability", journal = "Ann. Appl. Probab.", month = "04", number = "2", pages = "751--789", publisher = "The Institute of Mathematical Statistics", title = "Spatial Gibbs random graphs", url = "https://doi.org/10.1214/17-AAP1316", volume = "28", year = "2018" }

@ARTICLE{MDEW2018,

author = {Pap, E.J. and Boer, D. and Waalkens, H.}, title = {Non-Abelian nature of systems with multiple exceptional points}, journal = {Phys. Rev. A}, year = {2018}, volume = {98}, key = {published}, pages = {023818}, DOI = {10.1103/PhysRevA.98.023818}, URL = {https://link.aps.org/doi/10.1103/PhysRevA.98.023818}, abstract = {The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that upon encircling the EP eigenstates are permuted. As permutations of three or more objects form a non-abelian group, the question arises whether one can experimentally demonstrate this non-commutative behavior. This requires at least two EPs of a family of operators that have at least 3 eigenstates. Encircling two or more EPs poses the question of how to compose and combine the permutations. We address this problem using the theory of fundamental groups which also has a simple generalization to higher dimensional degeneracy structures like exceptional lines in a three-dimensional parameter space. A concrete implementation in a recently proposed PT symmetric waveguide system is suggested as an example of how to experimentally show the non-abelian nature of non-hermitian systems with multiple EPs.},

}

@article{prandi2018, author = {Prandi, D. and Rizzi, L. and Seri, M.}, doi = "10.4171/JST/226", journal = "Journal of Spectral Theory", volume = "8", number = "4", pages = " 1221--1280", title = "Quantum Confinement On Non-complete Riemannian Manifolds", url = "https://doi.org/10.4171/JST/226", year = "2018" }

@article{SnooWoracek2018, author = {H.S.V. de Snoo and H. Woracek}, journal = "Operator Theory: Adv. Appl.", pages = {425--483}, title = {Compressed resolvents, Q-functions and h_0-resolvents in almost Pontryagin spaces}, volume = "263", year = "2018" }

@article{DESNOO2018714, title = {The Krein formula in almost Pontryagin spaces. A proof via orthogonal coupling}, journal = "Indagationes Mathematicae", volume = "29", number = "2", pages = "714 - 729", year = "2018", issn = "0019-3577", doi = "https://doi.org/10.1016/j.indag.2017.12.001", url = "http://www.sciencedirect.com/science/article/pii/S0019357717301428", author = {de Snoo, H. and Woracek, H.}, abstract = "A new proof is provided for the Krein formula for generalized resolvents in the context of symmetric operators or relations with defect numbers (1,1) in an almost Pontryagin space. The new proof is geometric and uses the orthogonal coupling of the almost Pontryagin spaces induced by the Q-function and the parameter function in the Krein formula." }

@ARTICLE{Palasantzas2018,

author = {Tajik, Fatemeh and Sedighi, Mehdi and Masoudi, Amirali and Waalkens, Holger and Palasantzas, George}, title = {Dependence of chaotic behavior on optical properties and electrostatic effects in double beam torsional Casimir actuation}, year = {2018}, journal = {Phys. Rev. E}, volume = {98}, number = {2}, pages = {022210}, URL = {https://link.aps.org/doi/10.1103/PhysRevE.98.022210}, DOI = {10.1103/PhysRevE.98.022210}, key = {published}, abstract = {We investigate the influence of Casimir and electrostatic torques on double-beam torsional microelectromechanical systems with materials covering a broad range of conductivities of more than three orders of magnitude. For the frictionless autonomous systems, bifurcation and phase space analysis shows a significant difference between stable and unstable operating regimes for equal and unequal applied voltages on both sides of the double torsional system giving rise to heteroclinic and homoclinic orbits, respectively. For equal applied voltages, only the position of a symmetric unstable saddle equilibrium point is dependent on the material optical properties and electrostatic effects, while in any other case stable and unstable equilibrium points are dependent on both factors. For the periodically driven system, a Melnikov function approach is used to show the presence of chaotic motion rendering predictions of whether stiction or stable actuation will take place over long times impossible. Chaotic behavior introduces significant risk for stiction, and it is more likely to occur for the more conductive systems that experience stronger Casimir forces and torques. Indeed, when unequal voltages are applied, the sensitive dependence of chaotic motion on electrostatics is more pronounced for the highest conductivity systems.},

}

@article{SH:2018,

author = {Sterk, A.E. and M.P. Holland}, title = {Extreme value laws and mean squared error growth in dynamical systems}, journal = {Dynamics and Statistics of the Climate System: An Interdisciplinary Journal}, volume = {3}, year = {2018}, pages = {1-25}, section = {articles}, topic = {extremes}, doi = {10.1093/climsys/dzy007}, url = {https://dx.doi.org/10.1093/climsys/dzy007}

}

@ARTICLE{Palasantzas2017,

author = {Tajik, Fatemeh and Sedighi, Mehdi and Masoudi, Amirali and Waalkens, Holger and Palasantzas, George}, title = {Dependence of chaotic actuation dynamics of Casimir oscillators on optical properties and electrostatic effects}, journal = {EPJ B}, volume = {91}, issue = {4}, pages = {71}, year = {2018}, key = {published}, url = {https://doi.org/10.1140/epjb/e2018-80724-6}, abstract = {With Casimir and electrostatic forces playing a crucial role for the performance and stability of microelectromechanical systems (MEMS), the presence of chaotic behavior, which is often unavoidable, leads to device malfunction due to stiction. Therefore, we investigate here how the optical properties of different materials influence the chaotic behavior of electrostatic torsional MEMS due to changes in magnitude of the Casimir forces and associated torques. We consider the materials Au, which is a good conductor, AIST, which is a phase change material being close to metal in the crystalline state, and finally doped SiC as a very poor conductor. For the conservative systems without friction and driving, there is no chaotic behavior and the analysis of phase portraits and bifurcation diagrams reveal the strong sensitivity of stable actuation dynamics on the material optical properties, while applied electrostatic potentials lead faster to instability and stiction for higher conductivity materials. For the driven systems, the Melnikov method is used to study the presence of chaotic behavior. The results obtained from the Melnikov method are supported by the study of the contours of the transient time to stiction in the phase plane which reveal a substantially increased chaotic behavior for higher conductivity materials, associated with stronger Casimir torques, and applied electrostatic potentials. Because chaotic behavior prohibits long-term prediction of actuation dynamics, its precise understanding is crucial for the design of microdevices.}

}

%

2017

@Article{AlHdaibat17,

author = {Al-Hdaibat, B. and Govaerts, W. and Kekem, D.L. van and Kuznetsov, Yu.A.}, title = {Remarks on homoclinic structure in Bogdanov-Takens map}, journal = {Journal of Difference Equations and Applications}, pages = {1--13}, year = {2017}, doi = {doi:10.1080/10236198.2017.1329894}, url = {http://dx.doi.org/10.1080/10236198.2017.1329894},

}

@Article{Alvesetal2017, author={Alves, C. and Hil{\'a}rio, M. R. and De Lima, B. N. B. and Valesin, D.}, title="A Note on Truncated Long-Range Percolation with Heavy Tails on Oriented Graphs", journal="Journal of Statistical Physics", year="2017", month="Dec", day="01", volume="169", number="5", pages="972--980", abstract="We consider oriented long-range percolation on a graph with vertex set {\$}{\$}{\{}{\backslash}mathbb {\{}Z{\}}{\}}^d {\backslash}times {\{}{\backslash}mathbb {\{}Z{\}}{\}}{\_}+{\$}{\$} Z d {\texttimes} Z + and directed edges of the form {\$}{\$}{\backslash}langle (x,t), (x+y,t+1){\backslash}rangle {\$}{\$} ‚ü® ( x , t ) , ( x + y , t + 1 ) ‚ü© , for x,¬†y in {\$}{\$}{\{}{\backslash}mathbb {\{}Z{\}}{\}}^d{\$}{\$} Z d and {\$}{\$}t {\backslash}in {\{}{\backslash}mathbb {\{}Z{\}}{\}}{\_}+{\$}{\$} t ‚àà Z + . Any edge of this form is open with probability {\$}{\$}p{\_}y{\$}{\$} p y , independently for all edges. Under the assumption that the values {\$}{\$}p{\_}y{\$}{\$} p y do not vanish at infinity, we show that there is percolation even if all edges of length more than k are deleted, for k large enough. We also state the analogous result for a long-range contact process on {\$}{\$}{\{}{\backslash}mathbb {\{}Z{\}}{\}}^d{\$}{\$} Z d .", issn="1572-9613", doi="10.1007/s10955-017-1899-3", url="https://doi.org/10.1007/s10955-017-1899-3" }

@article{BissacotEndoEnter2017, title = "Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields ", journal = "Stochastic Processes and their Applications ", volume = "127", number = "12", pages = "4126 - 4138", year = "2017", note = "", issn = "0304-4149", doi = "https://doi.org/10.1016/j.spa.2017.03.023", url = "https://www.sciencedirect.com/science/article/pii/S0304414917301023", author = "Rodrigo Bissacot and Eric Ossami Endo and Aernout C.D. van Enter", keywords = "Ising model", keywords = "Cayley tree", keywords = "Inhomogeneous external fields", keywords = "Critical field", keywords = "Phase transition stability ", abstract = "Abstract We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev. " }

@ARTICLE{BoerWaalkens2017,

AUTHOR = {D. Boer and H. Waalkens}, JOURNAL = {Nederlands Tijdschrift voor Natuurkunde}, TITLE = {Het Groenewoldproduct}, PAGES = {54--57}, VOLUME = {2}, YEAR = {2017}, key = {published},

}

@ARTICLE{BoerWaalkens2017b,

AUTHOR = {D. Boer and H. Waalkens}, JOURNAL = {Dutch Journal of Physics}, TITLE = {The Groenewold product}, VOLUME = {1}, YEAR = {2017}, URL = {https://www.ntvn.nl/magazines/2017-1/The%20Groenewold%20product_1.html}, KEY = {published},

}

@Article{Boissonnatetal2017, author= {Boissonnat, J.-D. and Dyer, R. and Ghosh, A. and Martynchuk, N.}, title= {An Obstruction to Delaunay Triangulations in Riemannian Manifolds}, journal= {Discrete & Computational Geometry}, year="2017", month="Jul", day="06", abstract = "Delaunay has shown that the Delaunay complex of a finite set of points P of Euclidean space ℝm triangulates the convex hull of P, provided that P satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be defined for arbitrary Riemannian manifolds. However, Delaunay’s genericity assumption no longer guarantees that the Delaunay complex will yield a triangulation; stronger assumptions on P are required. A natural one is to assume that P is sufficiently dense. Although results in this direction have been claimed, we show that sample density alone is insufficient to ensure that the Delaunay complex triangulates a manifold of dimension greater than 2.", doi="10.1007/s00454-017-9908-5", url="https://doi.org/10.1007/s00454-017-9908-5" }

@BOOK{Broer2017,

AUTHOR = {H. W. Broer}, TITLE = {Near the Horizon: An Invitation to Geometric Optics}, PUBLISHER = {The Carus Mathematical Monographs (MAA)}, YEAR = {2017}

}

@Article{BroerZhao2017, author={Broer, Henk and Zhao, Lei}, title="De Sitter's theory of Galilean satellites", journal="Celestial Mechanics and Dynamical Astronomy", year="2017", month="Jan", day="01", volume="127", number="1", pages="95--119", abstract="In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by application of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter--Io--Europa--Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic librating orbits in both models for almost all choices of masses among which one sufficiently dominates the others.", issn="1572-9478", doi="10.1007/s10569-016-9718-8", url="https://doi.org/10.1007/s10569-016-9718-8" }

@article{ChattopadhyayVegterYap2017, title = "Certified computation of planar {M}orse-{S}male complexes ", journal = "Journal of Symbolic Computation ", volume = "78", pages = "3-40", year = "2017", note = "Algorithms and Software for Computational Topology ", issn = "0747-7171", doi = "http://dx.doi.org/10.1016/j.jsc.2016.03.006", url = "http://www.sciencedirect.com/science/article/pii/S0747717116300062", author = "Amit Chattopadhyay and Gert Vegter and Chee K. Yap", keywords = "Morse‚ÄìSmale complex", keywords = "Certified computation", keywords = "Interval arithmetic ", abstract = "Abstract The Morse‚ÄìSmale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse‚ÄìSmale complexes have been presented in case of piecewise linear manifolds (Edelsbrunner et al., 2003a). However, previous research in this field is incomplete in the case of smooth functions. In the current paper we address the following question: Given an arbitrarily complex Morse‚ÄìSmale system on a planar domain, is it possible to compute its certified (topologically correct) Morse‚ÄìSmale complex? Towards this, we develop an algorithm using interval arithmetic to compute certified critical points and separatrices forming the Morse‚ÄìSmale complexes of smooth functions on bounded planar domain. Our algorithm can also compute geometrically close Morse‚ÄìSmale complexes. " }

@article{Efstathiou2017,

Author = {Efstathiou, K. and Giacobbe, A. and Mardešić, P. and Sugny, D.}, Doi = {10.1063/1.4975215}, Journal = {Journal of Mathematical Physics}, Number = {2}, Pages = {022902}, Title = {Rotation forms and local Hamiltonian monodromy}, Url = {http://dx.doi.org/10.1063/1.4975215}, Volume = {58}, Year = {2017}, }

@article{EfstathiouMartynchuk2017, title = "Monodromy of Hamiltonian systems with complexity 1 torus actions", journal = "Journal of Geometry and Physics", volume = "115", number = "", pages = "104 - 115", year = "2017", note = "FDIS 2015: Finite Dimensional Integrable Systems in Geometry and Mathematical Physics", issn = "0393-0440", doi = "http://dx.doi.org/10.1016/j.geomphys.2016.05.014", url = "http://www.sciencedirect.com/science/article/pii/S0393044016301292", author = "K. Efstathiou and N. Martynchuk", }

@article{vanEnterLeNy2017, title = "Decimation of the Dyson‚ÄìIsing ferromagnet ", journal = "Stochastic Processes and their Applications ", volume = "127", number = "11", pages = "3776 - 3791", year = "2017", note = "", issn = "0304-4149", doi = "https://doi.org/10.1016/j.spa.2017.03.007", url = "http://www.sciencedirect.com/science/article/pii/S0304414917300807", author = "Aernout van Enter and Arnaud Le Ny", keywords = "Long-range Ising models", keywords = "Hidden phase transitions", keywords = "Generalized Gibbs measures ", abstract = "Abstract We study the decimation to a sublattice of half the sites of the one-dimensional Dyson‚ÄìIsing ferromagnet with slowly decaying long-range pair potentials of the form 1 | i ‚àí j | Œ± , deep in the phase transition region ( 1 < Œ± ‚â§ 2 and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ( Œ± > 2 ) and provides an example of a ‚Äústandard‚Äù non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations. " }

@article{HASSI20171019, title = "Extremal maximal sectorial extensions of sectorial relations", journal = "Indagationes Mathematicae", volume = "28", number = "5", pages = "1019 - 1055", year = {2017}, issn = "0019-3577", doi = "https://doi.org/10.1016/j.indag.2017.07.003", url = "http://www.sciencedirect.com/science/article/pii/S001935771730068X", author = "S. Hassi and A. Sandovici and H.S.V. de Snoo and H. Winkler", keywords = "Sectorial relation, Friedrichs extension, Kreƒ≠n extension, Extremal maximal sectorial extension" }

@article {MR3622284,

AUTHOR = {Kalle, Charlene and Kempton, Tom and Verbitskiy, Evgeny}, TITLE = {The random continued fraction transformation}, JOURNAL = {Nonlinearity}, FJOURNAL = {Nonlinearity}, VOLUME = {30}, YEAR = {2017}, NUMBER = {3}, PAGES = {1182--1203}, ISSN = {0951-7715}, MRCLASS = {37C40 (11K50 30B70)}, MRNUMBER = {3622284}, DOI = {10.1088/1361-6544/aa5243}, URL = {https://doi.org/10.1088/1361-6544/aa5243},

}

@article{KS:2017-perio,

author = {Van Kekem, Dirk and Sterk, Alef}, title = {Bifurcations and chaos in the {L}orenz-96 model}, journal = {Periodiek}, volume = {1}, year = {2017}, url = {http://perio.fmf.nl/archief/perio_2017-1.pdf#page=13}

}

@phdthesis{VladimirKrajnak2017, address = {Johann Bernoulli Institute for Mathematics and Computer Science}, annote = {Advisor: H. Waalkens, 153 pages}, author = {Krajnak, V.}, pages = {153}, school = {University of Groningen}, title = {Phase space geometry and invariant manifolds underlying reaction dynamics}, type = {PhD Dissertation}, url = {http://hdl.handle.net/11370/4d82d713-89ca-4efb-a12a-2607b91a54e7}, year = {2017} }

@article{KUOCH2017135, title = "A boundary driven generalized contact process with exchange of particles: Hydrodynamics in infinite volume", journal = "Stochastic Processes and their Applications", volume = "127", number = "1", pages = "135 - 178", year = "2017", issn = "0304-4149", doi = "https://doi.org/10.1016/j.spa.2016.06.004", url = "http://www.sciencedirect.com/science/article/pii/S0304414915300661", author = "Kevin Kuoch and Mustapha Mourragui and Ellen Saada", keywords = "Generalized contact process, Two species process, Hydrodynamic limit, Specific entropy, Stationary nonequilibrium states, Reservoirs, Infinite volume, Current", abstract = "We consider a two species process which evolves in a finite or infinite domain in contact with particle reservoirs at different densities, according to the superposition of a generalized contact process and a rapid-stirring dynamics in the bulk of the domain, and a creation/annihilation mechanism at its boundaries. For this process, we study the law of large numbers for densities and current. The limiting equations are given by a system of non-linear reaction‚Äìdiffusion equations with Dirichlet boundary conditions." }

@article{LevitValesin2017, author = {Levit, Anna and Valesin, Daniel}, doi = "10.1214/16-BJPS312", fjournal = "Brazilian Journal of Probability and Statistics", journal = "Braz. J. Probab. Stat.", month = "05", number = "2", pages = "254--274", publisher = "Brazilian Statistical Association", title = "Improved asymptotic estimates for the contact process with stirring", url = "http://dx.doi.org/10.1214/16-BJPS312", volume = "31", year = "2017" }

@article{LiLinEfstathiou2017,

Author = {Li, Pan and Lin, Wei and Efstathiou, Konstantinos}, Journal = {Chaos}, Number = {5}, Pages = {053103}, Title = {Isochronous dynamics in pulse coupled oscillator networks with delay}, Volume = {27}, Year = {2017}

}

@inproceedings{MBWS:2017,

author = {Maathuis, Henry and Boulogne, Luuk and Wiering, Marco and Sterk, Alef}, title = {Predicting chaotic time series using machine learning techniques}, booktitle = {Preproceedings of the 29th Benelux Conference on Artificial Intelligence (BNAIC 2017)}, month = {November}, year = {2017}, pages = {326--340}, publisher = {University of Groningen}, editor = {Bart Verheij and Marco Wiering}, url = {http://bnaic2017.ai.rug.nl/preproceedings.pdf#page=341}

}

@Article{Martynchuk2017, author={Martynchuk, N. and Efstathiou, K.}, title="Parallel Transport Along Seifert Manifolds and Fractional Monodromy", journal="Communications in Mathematical Physics", year="2017", month="Dec", day="01", volume="356", number="2", pages="427--449", abstract="The notion of fractional monodromy was introduced by Nekhoroshev, Sadovski{\'i} and Zhilinski{\'i} as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows one to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.", issn="1432-0916", doi="10.1007/s00220-017-2988-5", url="https://doi.org/10.1007/s00220-017-2988-5" }

@article{RathValesin2017, author = {Ráth, Balázs and Valesin, Daniel}, doi = "10.1214/16-AOP1104", fjournal = "The Annals of Probability", journal = "Ann. Probab.", month = "05", number = "3", pages = "1899--1951", publisher = "The Institute of Mathematical Statistics", title = "Percolation on the stationary distributions of the voter model", url = "http://dx.doi.org/10.1214/16-AOP1104", volume = "45", year = "2017" }

@article{RathValesin2017b, author = {Ráth, Balázs and Valesin, Daniel}, doi = "10.1214/17-ECP80", fjournal = "Electronic Communications in Probability", journal = "Electron. Commun. Probab.", pages = "12 pp.", pno = "50", publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", title = "On the threshold of spread-out voter model percolation", url = "https://doi.org/10.1214/17-ECP80", volume = "22", year = "2017" }

@Article{SchapiraValesin2017, author= {Schapira, B. and Valesin, D.}, title="Extinction time for the contact process on general graphs", journal="Probability Theory and Related Fields", year="2017", month="Dec", day="01", volume="169", number="3", pages="871--899", abstract="We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove, without any restriction on the graph G, that if the infection rate {\$}{\$}{\backslash}lambda {\$}{\$} $\lambda$ is larger than the critical rate of the one-dimensional process, then the extinction time grows faster than {\$}{\$}{\backslash}exp {\backslash}{\{}|G|/({\backslash}log |G|)^{\backslash}kappa {\backslash}{\}}{\$}{\$} exp {\{} | G | / ( log | G | ) $\kappa$ {\}} for any constant {\$}{\$}{\backslash}kappa > 1{\$}{\$} $\kappa$ > 1 , where |G| denotes the number of vertices of G. Also for general graphs, we show that the extinction time divided by its expectation converges in distribution, as the number of vertices tends to infinity, to the exponential distribution with parameter 1. These results complement earlier work of Mountford, Mourrat, Valesin and Yao, in which only graphs of bounded degrees were considered, and the extinction time was shown to grow exponentially in n; here we also provide a simpler proof of this fact.", issn="1432-2064", doi="10.1007/s00440-016-0742-0", url="https://doi.org/10.1007/s00440-016-0742-0" }

@article{SterkVKekem2017, author = {Sterk, A.E. and van Kekem, D.L.}, doi = "doi.org/10.1155/2017/9419024", journal = "Complexity", pages = "9419024", title = "Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity", url = "https://doi.org/10.1155/2017/9419024", abstract = "We introduce a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the attractor of the system. The predictability of an event is measured by comparing error growth rates for initial conditions leading to that event with all possible growth rates. We illustrate the method by studying the predictability of extreme amplitudes of traveling waves in the Lorenz-96 model. Our numerical experiments show that the predictability of extremes is affected by several routes to chaos in a different way. In a scenario involving intermittency due to a periodic attractor disappearing through a saddle-node bifurcation we find that extremes become better predictable as the intensity of the event increases. However, in a similar intermittency scenario involving the disappearance of a 2-torus attractor we find that extremes are just as predictable as nonextremes. Finally, we study a scenario which involves a 3-torus attractor in which case the predictability of extremes depends nonmonotonically on the prediction lead time.", year = "2017" }

@article{S:2017,

author = {Sterk, Alef}, title = {{Book review of ``Extremes and Recurrence in Dynamical Systems'' by Valerio Lucarini et al. (in Dutch)}}, journal = {Nieuw Archief voor Wiskunde}, volume = {18}, issue = {3}, pages = {218--218}, year = {2017}, url = {http://www.nieuwarchief.nl/serie5/toonnummer.php?deel=18&nummer=3&taal=0}

}

@article{Valesin:2017-perio,

author = {Daniel Valesin}, title = {The coupon-collector problem}, journal = {Periodiek}, volume = {3}, year = {2017},

}

@phdthesis{MohammadZaman2017, address = {Johann Bernoulli Institute for Mathematics and Computer Science}, annote = {Advisor: H. Waalkens and I. Hoveijn, 131 pages}, author = {Zaman, M.}, pages = {131}, school = {University of Groningen}, title = {Integral Manifolds of the Charged Three-Body Problem}, type = {PhD Dissertation}, url = {http://hdl.handle.net/11370/5af33a92-7e8a-43ef-aec0-9e97a1a593d7}, year = {2017} }

%

2016

@inproceedings{BogdanovTeullaudVegter2016, author = {Bogdanov, M. and Teillaud, M. and Vegter, G.}, booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)}, editor = {Leibniz International Proceedings in Informatics}, keywords = {covering spaces,finitely presented groups,fuchsian,hyperbolic surfaces}, pages = {20:1-20:17}, title = {{Delaunay triangulations on orientable surfaces of low genus}}, url = {http://drops.dagstuhl.de/opus/volltexte/2016/5912/pdf/LIPIcs-SoCG-2016-20.pdf}, year = {2016} }

@Misc{Broer2016,

title = {Laudatie voor John Mather (Uitreiking Brouwermedaillie 2014)}, author = { Broer, H.W. }, school = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, year = 2016, address = {The Netherlands}, howpublished = {Nieuw Archief voor Wiskunde 5/17:19-20},

}

@Misc{Broer2016b,

title = {Laudatie voor Marius Crainic (Award ceremony N.G. de Bruin Prize)}, author = { Broer, H.W. }, school = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, year = 2016, address = {The Netherlands}, howpublished = {Nieuw Archief voor Wiskunde 5/17:105-106},

}

@Misc{Broer2016c,

title = {Alles beweegt, maar waarheen?}, author = { Broer, H.W. }, school = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, year = 2016, address = {The Netherlands}, howpublished = {Nieuw Archief voor Wiskunde 5/17:128-136},

}

@article{BroerHanssmann2016, title = "On Jupiter and his {G}alilean satellites: {L}ibrations of De {S}itter's periodic motions", journal = "Indagationes Mathematicae", volume = "27", number = "5", pages = "1305 - 1336", year = "2016", note = "Dynamics and Geometry ", issn = "0019-3577", doi = "http://dx.doi.org/10.1016/j.indag.2016.09.002", url = "//www.sciencedirect.com/science/article/pii/S0019357716300544", author = "Henk W. Broer and Heinz Han{\ss}mann", keywords = "Periodic orbit", keywords = "Quasi-periodic orbit", keywords = "KAM theory", keywords = "Celestial mechanics ", abstract = "The motion of Jupiter’s four Galilean satellites Io–Europa–Ganymedes–Callisto is subjected to an orbital 1:2:41:2:4–resonance of the former (and inner) three. Willem de Sitter in the early 20th century gave a mathematical explanation of this in a Newtonian framework. He found a family of stable periodic solutions by using the work of Poincaré. This paper briefly reviews De Sitter’s theory, and focuses on the underlying geometry of a suitable covering space, where we develop Kolmogorov–Arnold–Moser theory to find Lagrangean invariant tori excited by the normal modes of the De Sitter periodic orbits. In this way we find many librations near these periodic orbits that may well offer a more realistic explanation of the observations." }

@Article{BroerZhao2016, author= {Broer, H. W. and Zhao, L.}, title="De Sitter's theory of Galilean satellites", journal="Celestial Mechanics and Dynamical Astronomy", year="2016", pages="1--25", abstract="In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by application of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter--Io--Europa--Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic librating orbits in both models for almost all choices of masses among which one sufficiently dominates the others.", issn="1572-9478", doi="10.1007/s10569-016-9718-8", url="http://dx.doi.org/10.1007/s10569-016-9718-8" }

@Article{vanEnter2016, author={van Enter, A. C. D. and de~Lima, B. N. B. and Valesin, D.}, title="Truncated Long-Range Percolation on Oriented Graphs", journal="Journal of Statistical Physics", year="2016", volume="164", number="1", pages="166--173", abstract="We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.", issn="1572-9613", doi="10.1007/s10955-016-1538-4", url="http://dx.doi.org/10.1007/s10955-016-1538-4" }

@ARTICLE{Enter2016b,

AUTHOR = {A.C.D. van Enter}, JOURNAL = {Nederlands Tijdschrift voor Natuurkunde}, TITLE = {Editorial: Krijgt men genoeg van experts?}, YEAR = {2016}, PAGES = {330}, VOLUME = {10},

}

@inproceedings{FleurkeEnter2016, author = {Fleurke, S. and van Enter, A.C.D.}, booktitle = {Mathematical and Computational Methods}, volume = {1}, pages = {268--275}, title = {{Time-Dependent Particle Densities in Finite Particle Deposition Systems}}, url = {https://www.iaras.org/iaras/journals/caijmcm/time-dependent-particle-densities-in-finite-particle-deposition-systems}, year = {2016}, abstract = {This paper contains calculations of the time-dependent particle densities in multi-layer particle deposition systems without screening. Several calculation methods are used. These methods can be used to calculate densities in all layers and are demonstrated with a number of examples. The densities in deposition systems of size 3 and 5 are calculated up to the third layer. It is also proven that border sites tend to have a higher density than sites in the middle. This partly explains why finite-sized systems tend to reach higher packing densities in higher layers than in low layers.}, }

@article{GarstSterk2016,

author = {Garst, S. and Sterk, A.E.}, title = {The dynamics of a fold-and-twist map}, journal = {Indagationes Mathematicae}, volume = {27}, issue = {5}, pages = {1279--1304}, year = {2016}, section = {articles}, topic = {dynsys}, url = {http://dx.doi.org/10.1016/j.indag.2016.07.002}

}

@article {GoellSchmidtVerbitskiy2016,

AUTHOR = {G\"oll, Martin and Schmidt, Klaus and Verbitskiy, Evgeny}, TITLE = {A {W}iener lemma for the discrete {H}eisenberg group}, JOURNAL = {Monatsh. Math.}, FJOURNAL = {Monatshefte f\"ur Mathematik}, VOLUME = {180}, YEAR = {2016}, NUMBER = {3}, PAGES = {485--525}, ISSN = {0026-9255}, MRCLASS = {22D15 (22D25 37A45 37C85 46L57 47B38 54H20)}, MRNUMBER = {3513217},

MRREVIEWER = {Abdolrasoul Pourabbas},

DOI = {10.1007/s00605-016-0894-0}, URL = {http://dx.doi.org/10.1007/s00605-016-0894-0},

}

@incollection {GoellVerbitskiy2016,

AUTHOR = {G\"oll, Martin and Verbitskiy, Evgeny}, TITLE = {Homoclinic points of principal algebraic actions}, BOOKTITLE = {Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity}, SERIES = {Lect. Notes Appl. Math. Mech.}, VOLUME = {3}, PAGES = {251--292}, PUBLISHER = {Springer, [Cham]}, YEAR = {2016}, MRCLASS = {37C29 (37B50 70K44)}, MRNUMBER = {3468300},

MRREVIEWER = {Lennard F. Bakker},

DOI = {10.1007/978-3-319-26883-5_4}, URL = {http://dx.doi.org/10.1007/978-3-319-26883-5_4},

}

@BOOK{HHvSW2016,

AUTHOR = {H. Han{\ss}mann and I. Hoveijn and S. van Strien and H. Waalkens (editors)}, TITLE = {Dynamics and Geometry}, PUBLISHER = {Indagationes Mathematicae, 27(5): 1029--1336}, YEAR = {2016}

}

@article{HRS:2016,

author = {Holland, M.P. and Rabassa, P. and Sterk, A.E.}, title = {Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems}, journal = {Nonlinearity}, volume = {29}, issue = {8}, year = {2016}, pages = {2355--2394}, section = {articles}, url = {http://dx.doi.org/10.1088/0951-7715/29/8/2355}

}

@article{JardonKojakhmetovBroerRoussarie2016, title = "Analysis of a slow–fast system near a cusp singularity", journal = "Journal of Differential Equations", volume = "260", number = "4", pages = "3785-3843", year = "2016", url = "http://dx.doi.org/10.1016/j.jde.2015.10.045", author = {Jardón Kojakhmetov, H. and Broer, H.W. and Roussarie, R.}, abstract = "This paper studies a slow–fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. " }

@article{KuochRedig2016, title = "Ergodic theory of the symmetric inclusion process ", journal = "Stochastic Processes and their Applications ", volume = "126", number = "11", pages = "3480 - 3498", year = "2016", note = "", issn = "0304-4149", doi = "http://dx.doi.org/10.1016/j.spa.2016.05.002", url = "http://www.sciencedirect.com/science/article/pii/S030441491530034X", author = "Kevin Kuoch and Frank Redig", keywords = "Interacting particle systems", keywords = "Simple inclusion process", keywords = "Invariant measures", keywords = "Coupling ", abstract = "Abstract We prove the existence of a successful coupling for n particles in the symmetric inclusion process. As a consequence we characterise the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in the course of time to an invariant product measure. " }

@article{MartynchukWaalkens2016,

Author = {Martynchuk, N. and Waalkens, H.}, Title = {Knauf's {D}egree and {M}onodromy in {P}lanar

{P}otential {S}cattering },

Journal = {Regular and Chaotic Dynamics}, Volume = {21}, Number = {6}, Year = 2016, Pages = {697-706}, URL = {http://dx.doi.org/10.1134/S1560354716060095},

}

@article{Mountfordetal2016, title = "Exponential extinction time of the contact process on finite graphs ", journal = "Stochastic Processes and their Applications ", volume = "126", number = "7", pages = "1974 - 2013", year = "2016", url = "http://dx.doi.org/10.1016/j.spa.2016.01.001", author = "Thomas Mountford and Jean-Christophe Mourrat and Daniel Valesin and Qiang Yao", abstract = "Abstract We study the extinction time œÑ of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z , then, uniformly over all trees of degree bounded by a given number, the expectation of œÑ grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, œÑ divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett (2009), we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices. " }

@article{MountfordValesin2016, title = "Functional Central Limit Theorem for the Interface of the Symmetric Multitype Contact Process ", journal = " ALEA Lat. Am. J. Probab. Math. Stat.", volume = "13", number = "1", pages = "481–519", year = "2016", url = "http://alea.impa.br/english/index_v13.htm", author = "Thomas Mountford and Daniel Valesin", }

@article{Mourratetal2016, author = {Mourrat, Jean-Christophe and Valesin, Daniel}, doi = "10.1214/16-EJP4476", fjournal = "Electronic Journal of Probability", journal = "Electron. J. Probab.", pages = "17 pp.", pno = "31", publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", title = "Phase transition of the contact process on random regular graphs", url = "http://dx.doi.org/10.1214/16-EJP4476", volume = "21", year = "2016" }

@article{PranavEdelsbrunnerWeygaertVegter2016, author = {Pranav, P. and Edelsbrunner, H. and van de Weygaert, R. and Vegter, G. and Kerber, M. and Jones, B. and Wintraecken, M.}, title = {{The Topology of the Cosmic Web in Terms of Persistent Betti Numbers}}, journal = {Monthly Notices of the Royal Astronomical Society}, volume = {465}, pages = {4281--4310}, year = {2016}, url = {http://mnras.oxfordjournals.org/content/early/2016/11/10/mnras.stw2862.abstract?keytype=ref&ijkey=O4RZOiK2hizkIra} }

@article {ShiraiVerbitskiy2016,

AUTHOR = {Shirai, Tomoyuki and Verbitskiy, Evgeny}, TITLE = {Solvable and algebraic systems on infinite ladder}, JOURNAL = {Indag. Math. (N.S.)}, FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series}, VOLUME = {27}, YEAR = {2016}, NUMBER = {5}, PAGES = {1162--1183}, ISSN = {0019-3577}, MRCLASS = {60K35 (37K60 82B20)}, MRNUMBER = {3573754}, DOI = {10.1016/j.indag.2016.02.003}, URL = {http://dx.doi.org/10.1016/j.indag.2016.02.003},

}

@Article{deSnooWoracek2016, author= {H.S.V. de Snoo and H. Woracek}, title="Restriction and factorization for isometric and symmetric operators in almost Pontryagin spaces", journal="Operator Theory Adv. Appl.", year="2016", volume="252", pages="123--170", }

@article{Sterk2016,

author = {Sterk, A.E.}, title = {Extreme amplitudes of a periodically forced {D}uffing oscillator}, journal = {Indagationes Mathematicae}, volume = {27}, issue = {5}, pages = {1059--1067}, year = {2016}, section = {articles}, topic = {extremes}, url = {http://dx.doi.org/10.1016/j.indag.2015.11.014}

}

@article{SSHM:2016,

author = {Sterk, A.E. and Stephenson, D.B. and Holland, M.P. and Mylne, K.R.}, title = {On the predictability of extremes: does the butterfly effect ever decrease?}, journal = {Quarterly Journal of the Royal Meteorological Society}, volume = {142}, issue = {694}, year = {2016}, pages = {58--64}, url = {http://onlinelibrary.wiley.com/doi/10.1002/qj.2627/abstract},

}

@article{SzaboValesin2016, author = {Szab{\'o}, R. and Valesin, D.}, doi = "10.1214/16-ECP11", fjournal = "Electronic Communications in Probability", journal = "Electron. Commun. Probab.", pages = "8 pp.", pno = "54", publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", title = "From survival to extinction of the contact process by the removal of a single edge", url = "http://dx.doi.org/10.1214/16-ECP11", volume = "21", year = "2016", }

@Article{SzaboVeto2016, author= {Szab{\'o}, R{\'e}ka and Vető, B{\'a}lint}, title="Ages of Records in Random Walks", journal="Journal of Statistical Physics", year="2016", volume="165", number="6", pages="1086--1101", issn="1572-9613", doi="10.1007/s10955-016-1671-0", url="http://dx.doi.org/10.1007/s10955-016-1671-0", }

@article {Verbitskiy2016,

AUTHOR = {Verbitskiy, Evgeny}, TITLE = {Thermodynamics of the binary symmetric channel}, JOURNAL = {Pac. J. Math. Ind.}, FJOURNAL = {Pacific Journal of Mathematics for Industry}, VOLUME = {8}, YEAR = {2016}, PAGES = {Art. 2, 9}, ISSN = {2198-4115}, MRCLASS = {37D35 (60J20 94A05)}, MRNUMBER = {3481196}, DOI = {10.1186/s40736-015-0021-5}, URL = {http://dx.doi.org/10.1186/s40736-015-0021-5},

}

%

2015

@ARTICLE{BaakeLenzvanEnter2015,

AUTHOR = {M. Baake and D. Lenz and A. C. D. van Enter}, TITLE = {Dynamical versus diffraction spectrum for structures with finite local complexity}, JOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {35}, PAGES = {2017--2043}, YEAR = {2015}, URL = {http://dx.doi.org/10.1017/etds.2014.28}, ABSTRACT = {It is well known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.}

}

@ARTICLE{Broer2015,

AUTHOR = {H. W. Broer}, TITLE = {Near-Horizon Celestial Phenomena, a Study in Geometric Optics}, JOURNAL = {Acta Applicandae Mathematicae}, VOLUME = {137}, PAGES = {17--39}, YEAR = {2015}, URL = {http://dx.doi.org/10.1007/s10440-014-9989-6}, ABSTRACT = {Near horizon phenomena, like blank strips in the setting sun or Fata Morganas, can be largely understood in terms of geometric optics. Here the existence of a warm layer above the observer in which light rays can be either refracted of reflected, already suffices to explain many of the phenomena; a reasoning which goes back to Alfred Wegener in the 1920’s. We review this theory, where first the atmosphere is divided into discrete, optically homogeneous layers, and where later the atmosphere is considered as a continuous, isotropic medium. Thus the theory gets embedded in differential geometry, where light rays are geodesics. A simplifying assumption is that the refraction index only depends on the elevation above the surface of the earth. Here a connection is made with the geodesic problem on a surface of revolution. In the background of this we touch the variational calculus as this runs from Bernoulli to Hamilton, all the way maintaining a completely anachronistic viewpoint.}

}

@ARTICLE{BWSKP2015,

author = {Broer, W. and Waalkens, H. and Svetovoy, V.B. and Knoester, J. and Palasantzas, G.},

title = {Nonlinear actuation dynamics of Casimir oscillators in the presence of surface roughness}, journal = {Phys. Rev. Applied},

year = {2015}, volume = {4}, pages = {054016},

url = {https://journals.aps.org/prapplied/accepted/78070A39Wb81f90780731013c5385d3358dac75db},

abstract = {At separations below 100 nm, Casimir forces strongly influence the actuation dynamics of micro- electromechanical systems (MEMS) in dry vacuum conditions. For a micron size plate oscillating near a surface, which mimics a frequently used setup in experiments with MEMS, we show that the roughness of the surface significantly influences the qualitative dynamics of the oscillator. Via a combination of analytical and numerical methods, it is shown that surface roughness leads to a clear increase of initial conditions associated with chaotic motion, that eventually lead to stiction of the plate on the surface. Since stiction leads to malfunction of MEMS oscillators our results are of central interest for the design of microdevices. Moreover, it is of significance for fundamentally motivated experiments performed with MEMS.}

}

@inproceedings{DyerVegterWintraecken2015, abstract = {We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbit- rary finite dimension, and exploit these simplices to obtain criteria for triangulating compact Riemannian manifolds. These geometric simplices are defined using Karcher means. Given a finite set of vertices in a convex set on the manifold, the point that minimises the weighted sum of squared distances to the vertices is the Karcher mean relative to the weights. Using barycentric coordinates as the weights, we obtain a smooth map from the standard Euclidean simplex to the manifold. A Riemannian simplex is defined as the image of the standard simplex under this bary- centric coordinate map. In this work we articulate criteria that guarantee that the barycentric coordinate map is a smooth embedding. If it is not, we say the Riemannian simplex is degenerate. Quality measures for the ‚Äúthickness‚Äù or ‚Äúfatness‚Äù of Euclidean simplices can be adapted to apply to these Riemannian simplices. For manifolds of dimension 2, the simplex is non-degenerate if it has a positive quality measure, as in the Euclidean case. However, when the dimension is greater than two, non-degeneracy can be guaranteed only when the quality exceeds a positive bound that depends on the size of the simplex and local bounds on the absolute values of the sectional curvatures of the manifold. An analysis of the geometry of non-degenerate Riemannian simplices leads to conditions which guarantee that a simplicial complex is homeomorphic to the manifold.}, url = {http://drops.dagstuhl.de/opus/volltexte/2015/5136/pdf/53.pdf}, author = {Dyer, R and Vegter, G and Wintraecken, M.H.M.J.}, booktitle = {Proceedings 31st International Symposium on Computational Geometry (SOCG 2015)}, keywords = {Karcher means,Riemannian manifold,Riemannian simplices,barycentric coordinates,triangulation}, month = July, pages = {255--269}, publisher = {Leibniz International Proceedings in Informatics}, title = {{Riemannian simplices and triangulations}}, doi={http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.255}, year = {2015} }

@article{DyerVegterWintraecken2015b, year={2015}, issn={0046-5755}, journal={Geometriae Dedicata}, doi={10.1007/s10711-015-0069-5}, title={Riemannian simplices and triangulations}, url={http://dx.doi.org/10.1007/s10711-015-0069-5}, publisher={Springer Netherlands}, keywords={Riemannian centre of mass; Karcher means; Barycentric coordinates; Triangulation; Riemannian manifold; Sampling conditions; Riemannian simplices; 57R05}, author={Dyer, R. and Vegter, G. and Wintraecken, M.H.M.J.}, pages={1-48}, number = {1}, volume = {179} }

@article{EfstathiouLiuBroer2015,

Author = {Efstathiou, Konstantinos and Liu, Xia and Broer, Henk W.}, Journal = {SIAM Journal on Applied Dynamical Systems}, Number = {2}, Pages = {914-941}, Title = {The {B}oundary-{H}opf-{F}old Bifurcation in {F}ilippov Systems}, Volume = {14}, Year = {2015}, URL = {http://dx.doi.org/10.1137/140988887}, Abstract = {This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields, for example, mechanical and electrical engineering, and ecology. The BHF bifurcation appears in a subclass of Filippov systems that we call Hopf-transversal systems. In such systems an equilibrium of one vector field goes through a Hopf bifurcation while the other vector field is transversal to the boundary. Depending on the slope of the transversal vector field, different bifurcation scenarios take place. The BHF bifurcation occurs at a critical value of the slope that separates these scenarios. We derive a local normal form for the BHF bifurcation and show the eight different associated bifurcation diagrams. The local 3-parameter normal form topologically models the simplest way to generically unfold the BHF bifurcation. The BHF bifurcation is then studied in a particular example from population dynamics.}

}

@phdthesis{JardonKojakhmetov2015, address = {Johann Bernoulli Institute for Mathematics and Computer Science}, annote = {Advisor: H. W. Broer and G. Vegter, 164 pages}, author = {Jard{\'o}n Kojakhmetov, H.}, pages = {164}, school = {University of Groningen}, title = {Classification of constrained differential equations embedded in the theory of slow fast systems: A$_k$ singularities and geometric desingularization}, type = {PhD Dissertation}, url = {https://www.rug.nl/research/portal/publications/classification-of-constrained-differential-equations-embedded-in-the-theory-of-slow-fast-systems(22311750-311e-43f4-96fc-a42c5b784505).html}, year = {2015} }

@InProceedings{FleurkevanEnter2015,

author = {S. Fleurke and A. C. D. van Enter}, title = {Multiple-Layer Parking with Screening}, booktitle = {Proceedings of the 2015 International Conference on Pure Mathematics, Applied Mathematics and Computational Methods (PMAMCM 2015)}, year = 2015, pages = {22--26}, Editors = {I. J. Rudas}, publisher = {RECENT ADVANCES in MATHEMATICS},

}

@InProceedings{HassiDeSnoo2015,

author = {S. Hassi and H.S.V. de Snoo}, title = {Factorization, majorization, and domination for linear relations}, booktitle = {Anniversary Volume in Honour of Professor Sebesty\'en }, year = 2015, Volume = 58, pages = {55--72}, publisher = {Annales Univ. Sci. Budapest},

}

@article{Martynchuk2015,

author = {Martynchuk, N.N.}, title = {Semi-local {L}iouville equivalence of complex {H}amiltonian systems defined by rational {H}amiltonian}, doi = {10.1016/j.topol.2015.05.090}, journal = {Topology and its Applications}, pages = {119-130}, volume = {191}, year = {2015},

}

@INPROCEEDINGS{MorozovSieberWaalkens2015,

AUTHOR = {Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Resonances and emission patterns of optical microdisk resonators with scatterers}, BOOKTITLE = {17th International Conference on Transparent Optical Networks (ICTON), 2015}, PAGES = {1--4}, YEAR = {2015}, URL = {http://dx.doi.org/10.1109/ICTON.2015.7193642}, key = {published}, abstract = { Optical microdisk resonators with circular boundaries support whispering gallery modes (WGMs) that travel along the boundary. Due to their extremely high Q-factors they have found many applications in, e.g., low-threshold lasing, the sensing of nanoparticles, optical filtering, and nonlinear optics. Recently, it has been demonstrated that the placement of a small scatterer within the microdisk can lead to highly directional modes in various frequency regimes while keeping the high Q-factors. The scatterer lifts the degeneracy of the pairs of clockwise and counter-clockwise propagating modes of the unperturbed circular disk and leads to two standing wave modes. The frequency of the first mode is affected by the scatterer whereas the second mode has a nodal line at the position of the scatterer and its frequency is left unaffected. As a result, more than one scatterer is needed if one wants to change the frequencies of both modes of a degenerate pair. We apply a Green's function method that is based on self-adjoint extension theory for point scatterers to compute the resonant modes with high efficiency and in a systematic way. We show that the placement of two or more scatterers can be used to split the emission into several chosen directions. }

}

@phdthesis{Pranav2015, address = {Johann Bernoulli Institute for Mathematics and Computer Science}, annote = {Advisor: M.A.M. van de Weygaert, G. Vegter and B.J.T. Jones, 332 pages}, author = {Pranav, P.}, pages = {298}, school = {University of Groningen}, title = {{Persistent holes in the Universe: A hierarchical topology of the cosmic mass distribution}}, type = {PhD Dissertation}, url = {http://www.rug.nl/research/portal/publications/persistent-holes-in-the-universe(f222529b-3215-4a1d-ad3b-81f660af2ebd).html}, year = {2015} }

@article{Sterk2015,

author = {Sterk, A.E.}, title = {De voorspelbaarheid van weersextremen}, journal = {De Physicus}, volume = {26}, issue = {1}, year = {2015}, pages = {44--46}

}

@phdthesis{Wintraecken2015, address = {Johann Bernoulli Institute for Mathematics and Computer Science}, annote = {Advisor: G. Vegter and M.A.M. van de Weygaert, 332 pages}, author = {Wintraecken, M.H.M.J.}, pages = {332}, school = {University of Groningen}, title = {{Ambient and intrinsic triangulations, and topological methods in cosmology}}, type = {PhD Dissertation}, url = {https://www.rug.nl/research/portal/publications/ambient-and-intrinsic-triangulations-and-topological-methods-in-cosmology(a199157d-778f-4c24-ab71-9c8faddd47e2).html}, year = {2015} }

@article{WintraeckenVegter2014, year={2015}, issn={1661-8270}, journal={Mathematics in Computer Science}, volume={9}, number={3}, doi={10.1007/s11786-014-0216-7}, title={On the Optimal Triangulation of Convex Hypersurfaces, Whose Vertices Lie in Ambient Space}, url={http://dx.doi.org/10.1007/s11786-014-0216-7}, publisher={Springer Basel}, keywords={Asymptotic approximations; Best approximation; Triangulation; Primary 41A60; 41A50; 32B25; Secondary 41A63; 65D17; 65D18; 68U05; 68U07}, author={Wintraecken, M.H.M.J. and Vegter, G.}, pages={345-353}, language={English} }

%

2014

@ARTICLE{BHdSW2014,

AUTHOR = {J. Behrndt and S. Hassi and H.S.V. de~Snoo and H.L. Wietsma}, TITLE = {Antitonicity of the inverse for selfadjoint matrices,

operators, and relations},

JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {142}, PAGES = {2783--2796}, YEAR = {2014}, URL = {http://dx.doi.org/10.1090/S0002-9939-2014-12115-0}, ABSTRACT = {Let $ H_1$ and $ H_2$ be selfadjoint operators or relations (multivalued operators) acting on a separable Hilbert space and assume that the inequality $ H_1 \leq H_2$ holds. Then the validity of the inequalities $ -H_1^{-1} \le -H_2^{-1}$ and $ H_2^{-1} \le H_1^{-1}$ is characterized in terms of the inertia of $ H_1$ and $ H_2$. Such results are known for matrices and boundedly invertible operators. In the present paper those results are extended to selfadjoint, in general unbounded, not necessarily boundedly invertible, operators and, more generally, for selfadjoint relations in separable Hilbert spaces. }

}

@ARTICLE{BDG2014,

AUTHOR = {J.-D. Boissonnat and R. Dyer and A. Ghosh}, TITLE = {Delaunay stability via perturbations}, JOURNAL = {International Journal of Computational Geometry & Applications}, VOLUME = {24}, PAGES = {125--152}, YEAR = {2014}, URL = {http://dx.doi.org/10.1142/S021819591450006X}, ABSTRACT = {We present an algorithm that takes as input a finite point set in Rm, and performs a per- turbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the weighting or refinement methods to remove poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but in addition it provides a guarantee of stability for the resulting triangulation. }

}

@MISC{Broer2014,

TITLE = {Review of 'Henri Poincar{\'e}: a scientific biography' by Jeremy Gray}, Author = {H. W. Broer}, SCHOOL = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, ADDRESS = {The Netherlands} YEAR = {2014}, HOWPUBLISHED = {BSHM Bulletin: Journal of the British Society for the History of Mathematics 29:1, 77-79}, URL = {http://dx.doi.org/10.1080/17498430.2014.855971}, ABSTRACT = {The theory of closed sesquilinear forms in the non-semi-bounded situation exhibits some new features, as opposed to the semi-bounded situation. In particular, there can be more than one closed form associated with the generalized Friedrichs extension S F of a non-semi-bounded symmetric operator S (if S F exists). However, there is one unique form [·, ·] satisfying Kato's second representation theorem and, in particular, dom = dom ∣S F∣1/2. In the present paper, another closed form [·, ·], also uniquely associated with S F, is constructed. The relation between these two forms is analysed and it is shown that these two non-semi-bounded forms can indeed differ from each other. Some general criteria for their equality are established. The results induce solutions to some open problems concerning generalized Friedrichs extensions and complete some earlier results about them in the literature. The study is connected to the spectral functions of definitizable operators in Kreĭn spaces.}

}

@ARTICLE{Broer2014b,

AUTHOR = {H. W. Broer}, TITLE = {Bernoulli's Light Ray Solution of the Brachistochrone Problem Through Hamilton's Eyes}, JOURNAL = {Int. J. Bifurcations Chaos}, VOLUME = {24}, PAGES = {1440009}, YEAR = {2014}, URL = {http://dx.doi.org/10.1142/S0218127414400094}, ABSTRACT = {This article contains a review of the brachistochrone problem as initiated by Johann Bernoulli in 1696–1697. As is generally known, the cycloid forms the solutions to this problem. We follow Bernoulli's optical solution based on the Fermat principle of least time and later rephrase this in terms of Hamilton's 1828 paper. Deliberately an anachronistic style is maintained throughout. Hamilton's solution recovers the cycloid in a way that is reminiscent of how Newton's mathematical principles imply Kepler's laws.}

}

@ARTICLE{CiftciWaalkensBroer2014,

AUTHOR = {Çiftçi, Ü. and Waalkens, H. and Broer, H. W.}, TITLE = {Cotangent bundle reduction and Poincaré-Birkhoff normal forms}, JOURNAL = {Physica D}, VOLUME = {268}, PAGES = {1--13}, YEAR = {2014}, URL = {http://dx.doi.org/10.1016/j.physd.2013.10.007},

}

@MISC{Dyer2014,

TITLE = {Non-flat Delaunay triangulations}, AUTHOR = {Dyer, R. }, SCHOOL = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, YEAR = {2014}, ADDRESS = {The Netherlands}, HOWPUBLISHED = {Periodiek, jaargang 2014, nummer 4, 30-37},

}

@INBOOK{ErmolaevVerbitskiy2014, author={V. Ermolaev and E. Verbitskiy }, TITLE ={Thermodynamic {G}ibbs {F}ormalism and {I}nformation Theory}, BOOKTITLE={The Impact of Applications on Mathematics},

EDITORS = {Masato Wakayama et al}, SERIES ={The Impact of Applications on Mathematics},

PUBLISHER = {Springer Japan}, year={2014}, vol={1}, pages={349-362 } }

@MISC{vanEnter2014,

TITLE = {Bootstrappercolatie}, AUTHOR = {van~Enter, A.C.D. }, SCHOOL = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, YEAR = {2014}, ADDRESS = {The Netherlands}, HOWPUBLISHED = {Periodiek, jaargang 2014, nummer 2, 26-29},

}

@ARTICLE{vanEnter2014b,

AUTHOR = {van~Enter, A.C.D.}, TITLE = {Aperiodicity in Equilibrium Systems: Between Order and Disorder }, JOURNAL = {Acta Physica Polonica A}, VOLUME = {126}, PAGES = {621--624}, YEAR = {2014}, URL = {http://dx.doi.org/10.12693/APhysPolA.126.621}, ABSTRACT = {Spatial aperiodicity occurs in various models and materials. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion and occurrence of aperiodic order in equilibrium statistical mechanics. In particular, we consider some spectral characterisations, and shortly review what is known about the occurrence of aperiodic order in lattice models at zero and nonzero temperatures. At the end some more speculative connections to the theory of (spin-)glasses are indicated.}

}

@INBOOK{vanEnterFleurke2014,

AUTHOR = {van~Enter, A.C.D. and Fleurke, S.}, TITLE = {Analytical Results for a Small Multilayer Parking System}, EDITOR = {Nikos Mastorakis, Valeri Mladenov}, BOOKTITLE = {Computational Problems in Engineering}, SERIES = {Lecture Notes in Electrical Engineering}, ADDRESS = {Switzerland}, PUBLISHER = {Springer International Publishing}, VOLUME = {307}, PAGES = {43--53}, YEAR = {2014}, URL = {http://link.springer.com/chapter/10.1007/978-3-319-03967-1_4}, Abstract = {In this article a multilayer parking system of size n=3 is studied. We prove that the asymptotic limit of the particle density in the center approaches a maximum of 1/2 in higher layers. This means a significant increase of capacity compared to the first layer where this value is 1/3. This is remarkable because the process is solely driven by randomness. We conjecture that this result applies to all finite parking systems with n ≥ 2.}

}

@ARTICLE{FHdSW2014,

AUTHOR = {A. Fleige and S. Hassi and H.S.V. de~Snoo and H. Winkler}, TITLE = {Non-semibounded closed symmetric forms associated

with a generalized Friedrichs extension},

JOURNAL = {Proc. Roy. Soc. Edinburg}, VOLUME = {144A}, PAGES = {731--745}, YEAR = {2014}, URL = {http://dx.doi.org/10.1017/S0308210512000108}

}

@article{GoellSchmidtVerbitskiy2014, author={M. G\"oll and K. Schmidt, K. and E. Verbitskiy}, title={Algebraic actions of the discrete Heisenberg group: Expansiveness and homoclinic points}, journal={Indagationes Mathematicae}, year={2014}, vol={25}, number={4}, pages={ 713-744} }

@ARTICLE{HdSS2014,

AUTHOR = {S. Hassi and H.S.V. de~Snoo and F.H. Szafraniec}, TITLE = {Normal intermediate extensions of symmetric relations}, JOURNAL = {Acta Math. Szeged}, VOLUME = {80}, PAGES = {195--232}, YEAR = {2014}, URL = {http://dx.doi.org/10.14232/actasm-013-008-0}, ABSTRACT = {Let S be a closed symmetric relation in a Hilbert space. If S is densely defined, then the normal extensions of S are selfadjoint. In general, normal nonselfadjoint intermediate extensions may not exist. Necessary and sufficient conditions for the existence of normal nonselfadjoint intermediate extensions are developed and all such extensions are parametrized.}

}

@article{JardonBroer2014, title = {Polynomial normal forms of constrained differential equations with three parameters}, journal = {Journal of Differential Equations}, volume = {257}, number = {4}, pages = {1012--1055}, year = {2014}, url = {http://dx.doi.org/10.1016/j.jde.2014.04.022}, author = {H. Jard{\'o}n-Kojakhmetov and Henk W. Broer}, abstract = {We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the Hyperbolic, and the Elliptic Umbilics. We provide polynomial local normal forms of \{CDEs\} under topological equivalence. Generic \{CDEs\} are important in the study of slow‚Äìfast (SF) systems. Many properties and the characteristic behavior of the solutions of \{SF\} systems can be inferred from the corresponding CDE. Therefore, the results of this paper show a first approximation of the flow of generic \{SF\} systems with three slow variables. } }

@inproceedings{Lien-Sharma-Vegter-Yap-2014, author = {Lien, Jyh-Ming and Sharma, Vikram and Vegter, Gert and Yap, Chee}, booktitle = {Proceedings Mathematical Software -- ICMS 2014}, number = {8592}, pages = {277--282}, series = {Springer Lecture Notes in Computer Science}, title = {{Isotopic Arrangement of Simple Curves: An Exact Numerical Approach Based on Subdivision}}, year = {2014} }

@ARTICLE{deSnooWinklerWojtylak2014,

AUTHOR = {H.S.V. de~Snoo and H. Winkler and M. Wojtylak}, TITLE = {Global and local behavior of zeros of nonnegative type}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {414}, PAGES = {273--284}, YEAR = {2014}, URL = {http://dx.doi.org/10.1016/j.jmaa.2014.01.004}, ABSTRACT = {A generalized Nevanlinna function image with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by image, image, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type image as a function of τ is being studied. In particular, it is shown that it is continuous and its behavior in the points where the function extends through the real line is investigated.}

}

@MISC{Sterk2014,

TITLE = {The statistics of extreme values in deterministic systems}, AUTHOR = {Sterk, A.E. }, SCHOOL = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, YEAR = {2014}, ADDRESS = {The Netherlands}, HOWPUBLISHED = {Periodiek, jaargang 2014, nummer 5, 26-28},

}

@ARTICLE{Zhao2014,

AUTHOR = {L. Zhao}, TITLE = {Quasi-periodic Solutions of the Spatial Lunar Three-body Problem}, JOURNAL = {Cel. Mech. Dyn. Astron.}, VOLUME = {119}, PAGES = {91--118}, YEAR = {2014}, URL = {http://dx.doi.org/10.1007/s10569-014-9549-4}, ABSTRACT = {In this paper, we consider the spatial lunar three-body problem in which one body is far away from the other two. By applying a well-adapted version of KAM theorem to Lidov–Ziglin’s global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar three-body problem.}

}

@ARTICLE{Zhao2014b,

AUTHOR = {L. Zhao}, TITLE = {Partial Reduction and Delaunay/Deprit coordinates}, JOURNAL = {Cel. Mech. Dyn. Astron.}, VOLUME = {120}, PAGES = {423--432}, YEAR = {2014}, URL = {http://dx.doi.org/10.1007/s10569-014-9584-1}, ABSTRACT = {The partial reduction procedure of the rotational symmetry of the N-body problem means to only fix the direction of the total angular momentum, leaving the norm of the total angular momentum unfixed and the rotational symmetry around this direction unreduced. In this article, we present a conceptual link between this procedure, appearing as an intermediate step in the total reduction procedure of the rotational symmetry, with the symplectic cross-section theorem of Guillemin–Sternberg. As an application of this link, we present some alternative proofs of the symplecticity of the Delaunay and Deprit coordinates, which are important symplectic coordinates in the perturbative study of celestial mechanics.}

}

%

2013

@article{BHSWW2013, Author = {Behrndt, J. and Hassi, S. and de~Snoo, H.S.V and Wietsma, H.L. and Winkler, H.}, Journal = {Complex Anal. Oper. Theory}, Title = {Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator}, Year = {2013}, Pages = {331--362}, Volume = {7} }

@BOOK{Broer2013,

AUTHOR = {Broer, H. W.}, TITLE = {Hemelverschijnselen nabij de Horizon}, PUBLISHER = {Epsilon Uitgaven}, YEAR = {2013},

}

@article{Broer2013b, Author = {Broer, H. W.}, Journal = {Nieuw Archief voor Wiskunde 5th series}, Title = {Bernoulli’s lichtstraal-oplossing van het brachistochrone probleem door de ogen van Hamilton}, Year = {2013}, Pages = {99--107}, Volume = {14}, Number = {2}, URL = {http://www.math.rug.nl/dsmp/pdf/hambern.pdf} }

@INBOOK{BroerHanssmannYou2013,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. and You, Y.}, TITLE = {On the destruction of resonant Lagrangean tori in Hamiltonian systems}, EDITOR = {Johann, A. and Kruse, H.-P. and Rupp, F. and Schmitz, S.}, BOOKTITLE = {Recent Trends in Dynamical Systems, Proceedings of a Conference in Honor of J\"urgen Scheurle}, SERIES = {Springer Proceedings in Mathematics \& Statistics}, ADDRESS = {Heidelberg}, PUBLISHER = {Springer}, VOLUME = {35}, PAGES = {Ch. 13}, YEAR = {2013}, URL = {http://www.springer.com/mathematics/dynamical+systems/book/978-3-0348-0450-9}

}

@article{BroerKaperKrupa2013, Author = {Broer, H. W. and Kaper, T. J. and Krupa, M.}, Journal = {J. Dyn. Diff. Equat.}, Title = {Geometric Desingularization of a Cusp Singularity in Slow–Fast Systems with Applications to Zeeman’s Examples}, Volume = {25}, Year = {2013}, Pages = {925--958}, URL = {http://dx.doi.org/10.1007/s10884-013-9322-5}, Abstract = {The cusp singularity—a point at which two curves of fold points meet—is a prototypical example in Takens’ classification of singularities in constrained equations, which also includes folds, folded saddles, folded nodes, among others. In this article, we study cusp singularities in singularly perturbed systems for sufficiently small values of the perturbation parameter, in the regime in which these systems exhibit fast and slow dynamics. Our main result is an analysis of the cusp point using the method of geometric desingularization, also known as the blow-up method, from the field of geometric singular perturbation theory. Our analysis of the cusp singularity was inspired by the nerve impulse example of Zeeman, and we also apply our main theorem to it. Finally, a brief review of geometric singular perturbation theory for the two elementary singularities from the Takens’ classification occurring for the nerve impulse example—folds and folded saddles—is included to make this article self-contained.} }

@article{BroerLeviSimo2013, Author = {Broer, H. W. and Levi, M. and Sim{\'o}, C.}, Journal = {Nonlinearity}, Title = {Large scale radial stability density of Hill’s equation}, Year = {2013}, Pages = {565--589}, Volume = {26}, URL = {http://dx.doi.org/10.1088/0951-7715/26/2/565}, Abstract = {This paper deals with large scale aspects of Hill’s equation $\ddot{x}+(a+bp(t))x=0$, where $p$ is periodic with a fixed period. In particular, the interest is the asymptotic radial density of the stability domain in the $(a,b)$-plane. It turns out that this density changes discontinuously in a certain direction and exhibits and interesting asymptotic fine structure. Most of the paper deals with the case where $p$ is a Morse function with one maximum and one minimum, but also the discontinuous case of square Hill’s equation is studied, where the density behaves differently.} }

@INBOOK{BroerVegter2013,

AUTHOR = {Broer, H.W. and Vegter, G.}, TITLE = {Resonance and singularities}, EDITOR = {Ibáñez, S. and Pérez del Río, J.S. and Pumariño, A. and Rodríguez, J.Á. }, BOOKTITLE = {Progress and Challenges in Dynamical Systems}, SERIES = {Springer Proceedings in Mathematics \& Statistics}, ADDRESS = {Heidelberg}, PUBLISHER = {Springer}, VOLUME = {54}, PAGES = {89--126}, YEAR = {2013}, URL = {http://www.springer.com/mathematics/dynamical+systems/book/978-3-642-38829-3}

}

@PHDTHESIS{Ciftci2013,

AUTHOR = {{\"U}nver \c{C}ift\c{c}i}, TITLE = {Cotangent bundle reduction and its application to Poincar{\'e}-Birkhoff normal forms}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {June}, YEAR = {2013}, NOTE = {Advisor: H. Waalkens, 96 pages}, URL = {http://irs.ub.rug.nl/ppn/357587812}

}

@article{CiftciWaalkens2013, Author = {\c{C}ift\c{c}i, {\"U}. and Waalkens, H.}, Journal = {Phys. Rev. Lett.}, Title = {Reaction Dynamics Through Kinetic Transition States}, Year = {2013}, Pages = {233201}, Volume = {110}, URL = {http://dx.doi.org/10.1103/PhysRevLett.110.233201}, Abstract = {The transformation of a system from one state to another is often mediated by a bottleneck in the system’s phase space. In chemistry, these bottlenecks are known as transition states through which the system has to pass in order to evolve from reactants to products. The chemical reactions are usually associated with configurational changes where the reactants and products states correspond, e.g., to two different isomers or the undissociated and dissociated state of a molecule or cluster. In this Letter, we report on a new type of bottleneck which mediates kinetic rather than configurational changes. The phase space structures associated with such kinetic transition states and their dynamical implications are discussed for the rotational vibrational motion of a triatomic molecule. An outline of more general related phase space structures with important dynamical implications is given.} }

@article{DuminilCopinEnter2013, Author = {Duminil-Copin, H. and van~Enter, A.C.D.}, Journal = {Ann. Prob.}, Title = {Sharp metastability threshold for an anisotropic bootstrap percolation model}, Year = {2013}, Pages = {1218--1242}, Volume = {41}, Number = {3A}, URL = {http://dx.doi.org/10.1214/11-AOP722}, Abstract = {Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following “anisotropic” bootstrap percolation model: the neighborhood of a point (m,n) is the set (m+2,n),(m+1,n),(m,n+1),(m−1,n),(m−2,n),(m,n−1). At time 0, sites are occupied with probability p. At each time step, sites that are occupied remain occupied, while sites that are not occupied become occupied if and only if three of more sites in their neighborhood are occupied. We prove that it exhibits a sharp metastability threshold. This is the first mathematical proof of a sharp threshold for an anisotropic bootstrap percolation model.} }

@article{EfstathiouBroer2013, Author = {K. Efstathiou and H. W. Broer}, Journal = {Comm. Math. Phys.}, Title = {Uncovering Fractional Monodromy}, Year = {2013}, Pages = {549--588}, Volume = {324}, URL = {http://dx.doi.org/10.1007/s00220-013-1816-9}, Abstract = {The uncovering of the role of monodromy in integrable Hamiltonian fibrations has been one of the major advances in the study of integrable Hamiltonian systems in the past few decades: on one hand monodromy turned out to be the most fundamental obstruction to the existence of global action-angle coordinates while, on the other hand, it provided the correct classical analogue for the interpretation of the structure of quantum joint spectra. Fractional monodromy is a generalization of the concept of monodromy: instead of restricting our attention to the toric part of the fibration we extend our scope to also consider singular fibres. In this paper we analyze fractional monodromy for n1:(-n2) resonant Hamiltonian systems with n1, n2 coprime natural numbers. We consider, in particular, systems that for n1, n2 > 1 contain one-parameter families of singular fibres which are ‘curled tori’. We simplify the geometry of the fibration by passing to an appropriate branched covering. In the branched covering the curled tori and their neighborhood become untwisted thus simplifying the geometry of the fibration: we essentially obtain the same type of generalized monodromy independently of n1, n2. Fractional monodromy is then recovered by pushing the results obtained in the branched covering back to the original system.} }

@Misc{Jong2013,

title = {KAM-theorie en de stabiliteit van het zonnestelsel}, author = { de Jong, T. }, school = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, year = 2013, address = {The Netherlands}, howpublished = {Nieuw Archief voor Wiskunde 5th series, 14(4):259-262},

}

@article {LindSchmidtVerbitskiy2013,

AUTHOR = {Lind, D. and Schmidt, K. and Verbitskiy, E.}, TITLE = {Homoclinic points, atoral polynomials, and periodic points of algebraic {$\Bbb Z^d$}-actions}, JOURNAL = {Ergodic Theory Dynam. Systems}, VOLUME = {33}, YEAR = {2013}, NUMBER = {4}, PAGES = {1060--1081}, URL = {http://dx.doi.org/10.1017/S014338571200017X}, Abstract = {Cyclic algebraic \${\mathbb {Z}^{d}}\$-actions are defined by ideals of Laurent polynomials in \$d\$ commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative \$d\$-torus. For such expansive actions it is known that the limit of the growth rate of periodic points exists and is equal to the entropy of the action. In an earlier paper the authors extended this result to ideals whose variety intersects the \$d\$-torus in a finite set. Here we further extend it to the case where the dimension of intersection of the variety with the \$d\$-torus is at most \$d-2\$. The main tool is the construction of homoclinic points which decay rapidly enough to be summable.}

}

@PHDTHESIS{Liu2013,

AUTHOR = {Xia Liu}, TITLE = {The discontinuous Hopf-transversal system and its geometric regularization}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {February}, YEAR = {2013}, NOTE = {Advisor: H. W. Broer, 96 pages}, URL = {http://irs.ub.rug.nl/ppn/354817590}

}

@Misc{SterkVitoloBroer2013,

title = {Het onvoorspelbare venijn van de staart}, author = { Sterk, A.E. and Vitolo, R. and Broer, H.W. }, school = {University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science}, year = 2013, address = {The Netherlands}, howpublished = {Nieuw Archief voor Wiskunde 5th series, 14(3):164-167}, url = {http://www.math.rug.nl/~broer/pdf/stvibr.pdf},

}

%

2012

@article{BehrndtHassiSnooWietsma2012, Author = {J. Behrndt and S. Hassi and H.S.V. de Snoo and H.L. Wietsma}, Journal = {Lin. Alg. Appl.}, Title = {Limit properties of monotone matrix functions}, Year = {2012}, Pages = {935--953}, Volume = {436} }

@article{Broer2012b, Author = {Broer, H.W.}, Journal = {NAW}, Title = {Perspectives on the legacy of Poincar{\'e} in the field of dynamical systems}, Year = {2012}, Pages = {201--208}, Volume = {5/13}, Number = {3}, URL = {http://www.math.rug.nl/~broer/pdf/poincare.pdf}, Abstract = {Henri Poincar{\'e} (1854–1912) has had a tremendous influence on the development of mathemat- ics and mathematical physics, the traces of which can be seen till the present day. This paper by Henk Broer attempts to highlight aspects of this legacy and its influence on certain more recent developments, focusing on the field of dynamical systems. His various approaches have invariably led to fruitful subfields, where geometry, algebra and later also measure theory are effectively at work in combination with analysis and calculus. } }

@article{Broer2012, Author = {Broer, H.W.}, Journal = {Acta Applicandae Mathematicae}, Title = {Resonance and Fractal Geometry}, Year = {2012}, Pages = {61--86}, Volume = {120}, Number = {1}, URL = {http://dx.doi.org/10.1007/s10440-012-9670-x}, Abstract = { The phenomenon of resonance will be dealt with from the viewpoint of dynam- ical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena occur for parameter values in fractal sets of positive measure. We describe a universal phenomenon that plays an important role in modelling. This paper gives a summary of the background theory, veined by examples. } }

@article{CiftciWaalkens2012, Author = {\c{C}ift\c{c}i, {\"U}. and Waalkens, H.}, Journal = {Nonlinearity}, Pages = {791--812}, Title = {Phase space structures governing reaction dynamics in rotating molecules}, Volume = {25}, Year = {2012}, URL = {http://dx.doi.org/10.1088/0951-7715/25/3/791}, ABSTRACT = {Recently, the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type equilibrium points which are characteristic for reaction type dynamics. Their construction is based on a Poincare ́–Birkhoff normal form. Using tools from the geometric theory of Hamiltonian systems and their reduction, we show in this paper how the construction of these phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced N-body system. As rotations almost always play an important role in the reaction dynamics of molecules, the approach presented in this paper is of great relevance for applications.} }

@INBOOK{DerkachHassiMalamudSnoo2012,

AUTHOR = {V.A. Derkach and S. Hassi and M.M. Malamud and H.S.V. de Snoo}, TITLE = {Boundary triplets and Weyl functions. Recent developments}, EDITOR = {Seppo Hassi, Hendrik S.V. de Snoo and Franciszek Hugon Szafraniec}, BOOKTITLE = {Operator Methods for Boundary Value Problems}, SERIES = {London Mathematical Society Lecture Note Series}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, VOLUME = {404}, PAGES = {161--220}, YEAR = {2012}

}

@article{DerkachHassiSnoo2012, Author = {V.A. Derkach and S. Hassi and H.S.V. de Snoo}, Journal = {Math. Nachr.}, Title = {The truncated moment problem}, Year = {2012}, Pages = {1741--1769}, Volume = {285} }

@article{EfstathiouGiacobbe2012,

Abstract = {In this paper we investigate the global geometry associated to cusp singular points of two-degree of freedom completely integrable systems. It typically happens that such singular points appear in couples, connected by a curve of hyperbolic singular points. We show that such a couple gives rise to two possible topological types as base of the integrable torus bundle, that we call pleat and flap. When the topological type is a flap, the system can have non-trivial monodromy, and this is equivalent to the existence in phase space of a lens space compatible with the singular Lagrangian foliation associated to the completely integrable system.}, Author = {Efstathiou, K. and Giacobbe, A.}, Doi = {10.1088/0951-7715/25/12/3409}, Journal = {Nonlinearity}, Number = 12, Pages = {3409-3422}, Title = {The topology associated to cusp singular points}, Volume = 25, Year = 2012

}

@MISC {Enter2012c,

AUTHOR = {van Enter, A.C.D.}, TITLE = {Book Review: Zekerheden in waarnemingen. Natuurwetenschappelijke ontwikkelingen in Nederland rond 1900}, HOWPUBLISHED = {Nieuw Archief voor Wiskunde, 13, 289--290}, YEAR = {2012},

}

@article{Enter2012, Author = {van~Enter, A.C.D.}, Journal = {Nederlands Tijdschrift voor Natuurkunde}, Title = {Tijd in machten van tien}, Year = {2012}, Pages = {70}, Volume = {78} }

@article{Enter2012b, Author = {van~Enter, A.C.D.}, Journal = {IAMP News Bulletin}, Title = {On the prevalence of non-Gibbsian states in mathematical physics}, Year = {2012}, Pages = {15--24}, Volume = {April 2012}, URL = {http://www.iamp.org/bulletins/Bulletin-April12.pdf}, Abstract = {Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances one encounters measures that are not of Gibbsian form. We present here a number of examples of such non-Gibbsian measures, and discuss some of the underlying mathematical and physical issues to which they gave rise.} }

@article{EnterErmolaevIacobelliKuelske2012, Author = {van Enter, A.C.D. and Ermolaev, V. N. and Iacobelli, G. and K{\"u}lske, C.}, Journal = {Ann. Inst. H. Poincar{\'e} Probab. Statist.}, Title = {Gibbs–non-Gibbs properties for evolving Ising models on trees}, Year = {2012}, Pages = {774--791}, Volume = {48}, Number = {3}, URL = {http://dx.doi.org/10.1214/11-AIHP421}, Abstract = {In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each state there are two transitions. For the intermediate state there is a transition from a Gibbsian regime to a non-Gibbsian regime where some, but not all configurations are bad, and a second one to a regime where all configurations are bad.

For the plus and minus state, the two transitions are from a Gibbsian regime to a non-Gibbsian one and then back to a Gibbsian regime again. } }

@article{EnterFey2012, Author = {van Enter, A.C.D. and Fey, A.}, Journal = {J. Stat. Phys.}, Title = {Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions}, Year = {2012}, Pages = {97--112}, Volume = {147}, URL = {http://dx.doi.org/10.1007/s10955-012-0455-4}, Abstract = {In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the ‘easiest growth direction’ in the model. In contrast to anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metastability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.} }

@article{EnterIacobelliTaati2012, Author = {van~Enter, A.C.D. and Iacobelli, G. and Taati, S.}, Journal = {Rev. Math. Phys.}, Title = {POTTS MODEL WITH INVISIBLE COLORS: RANDOM-CLUSTER REPRESENTATION AND PIROGOV–SINAI ANALYSIS}, Year = {2012}, Pages = {1250004}, Volume = {24}, URL = {http://dx.doi.org/10.1142/S0129055X12500043}, Abstract = {We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among q "visible" colors along with the presence of r non-interacting "invisible" colors. We introduce a random-cluster representation for the model, for which we prove the existence of a first-order transition for any q > 0, as long as r is large enough. When q > 1, the low-temperature regime displays a q-fold symmetry breaking. The proof involves a Pirogov–Sinai analysis applied to this random-cluster representation of the model.} }

@INBOOK{HassiSchaftSnooZwart2012,

AUTHOR = {S. Hassi and A.J van der Schaft and H.S.V. de Snoo and H. Zwart}, TITLE = {Dirac structures and boundary relations}, EDITOR = {Seppo Hassi, Hendrik S.V. de Snoo and Franciszek Hugon Szafraniec}, BOOKTITLE = {Operator Methods for Boundary Value Problems}, SERIES = {London Mathematical Society Lecture Note Series}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, VOLUME = {404}, PAGES = {259--274}, YEAR = {2012}

}

@article{HassiSnooSzafraniec2012, Author = {S. Hassi and H.S.V. de Snoo and F.H. Szafraniec}, Journal = {Indag. Math.}, Pages = {1087--1117}, Title = {Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations}, Volume = {23}, Year = {2012} }

@BOOK{HassiSnooSzafraniec2012b,

AUTHOR = {S. Hassi and H.S.V. de Snoo and F.H. Szafraniec (editors)}, TITLE = {Operator methods for boundary value problems}, PUBLISHER = {Cambridge University Press}, SERIES = {London Mathematical Society Lecture Note Series}, VOLUME = {404}, YEAR = {2012},

}

@INBOOK{HassiSnooSzafraniec2012c,

AUTHOR = {S. Hassi and H.S.V. de Snoo and F.H. Szafraniec}, TITLE = {John Williams Calkin: a short biography}, EDITOR = {Seppo Hassi, Hendrik S.V. de Snoo and Franciszek Hugon Szafraniec}, BOOKTITLE = {Operator Methods for Boundary Value Problems}, SERIES = {London Mathematical Society Lecture Note Series}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, VOLUME = {404}, PAGES = {1--2}, YEAR = {2012}

}

@PHDTHESIS{Iacobelli2012,

AUTHOR = {Iacobelli, G.}, TITLE = {Metastates, non-Gibbsianness and Phase Transitions: a stroll through statistical mechanics}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {February}, YEAR = {2012}, NOTE = {Advisors: A.C.D. van Enter and C. K{\"u}lske, 158 pages}, URL = {http://irs.ub.rug.nl/ppn/339773758}

}

@inproceedings{KariTaati2012,

AUTHOR = {J. Kari and S. Taati}, TITLE = {Conservation laws and invariant measures in surjective cellular automata}, BOOKTITLE = {Proceedings of AUTOMATA-2011, DMTCS}, PAGES = {113--122}, YEAR = {2012}, URL = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAP0108/3771}, ABSTRACT = {We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.}

}

@article{LSSW2012, Author = {J.-Ph. Labrousse and A.~Sandovici and H.S.V. de Snoo and H.~Winkler}, Journal = {Operators and Matrices}, Title = {Closed linear relations and their regular points}, Year = {2012}, Pages = {681--714}, Volume = {6} }

@article{SnooWoracek2012, Author = {H.S.V. de Snoo and H. Woracek}, Journal = {Lin. Alg. Appl.}, Title = {Sums, couplings, and completions of almost Pontryagin spaces}, Year = {2012}, Pages = {559--580}, Volume = {437} }

@article{SHRBV2012, Author = {Sterk, A. and Holland, M.P. and Rabassa, P. and Broer, H.W. and Vitolo, R.}, Journal = {Nonlin. Processes Geophys.}, Pages = {529--539}, Title = {Predictability of extreme values in geophysical models}, Volume = {19}, Year = {2012}, URL = {http://dx.doi.org/10.5194/npg-19-529-2012}, ABSTRACT = {Extreme value theory in deterministic systems is concerned with unlikely large (or small) values of an observable evaluated along evolutions of the system. In this paper we study the finite-time predictability of extreme values, such as convection, energy, and wind speeds, in three geophysical models. We study whether finite-time Lyapunov exponents are larger or smaller for initial conditions leading to extremes. General statements on whether extreme values are better or less predictable are not possible: the predictability of extreme values depends on the observable, the attractor of the system, and the prediction lead time.} }

@article{Thomas2012, Author = {E. G. F. Thomas}, Journal = {Quaestiones Mathematicae}, Title = {Vector integration}, Year = {2012}, Pages = {391--416}, Volume = {35}, Number = {4}, URL = {http://dx.doi.org/10.2989/16073606.2012.742230}, Abstract = {This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving adequate convergence theorems, and establishing usable integrability criteria. The aim is to give an account that is both general, comprising all previously known formulations, and sufficiently simple, perhaps to be of use even to those who are interested only in the case of Banach space.} }

@article{YEII2012,

Abstract = {Data selection is a fundamental task in visualization because it serves as a pre-requisite to many follow-up interactions. Efficient spatial selection in 3D point cloud datasets consisting of thousands or millions of particles can be particularly challenging. We present two new techniques, TeddySelection and CloudLasso, that support the selection of subsets in large particle 3D datasets in an interactive and visually intuitive manner. Specifically, we describe how to spatially select a subset of a 3D particle cloud by simply encircling the target particles on screen using either the mouse or direct-touch input. Based on the drawn lasso, our techniques automatically determine a bounding selection surface around the encircled particles based on their density. This kind of selection technique can be applied to particle datasets in several application domains. TeddySelection and CloudLasso reduce, and in some cases even eliminate, the need for complex multi-step selection processes involving Boolean operations. This was confirmed in a formal, controlled user

study in which we compared the more flexible CloudLasso

technique to the standard cylinder-based selection technique. This study showed that the former is consistently more efficient than the latter; in several cases the CloudLasso selection time was half that of the corresponding cylinder-based selection.}, Author = {Yu, L. and Efstathiou, K. and Isenberg, P. and Isenberg, T.}, Doi = {10.1109/TVCG.2012.217}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Number = 12, Pages = {2245-2254}, Title = {Efficient Structure-Aware Selection Techniques for 3D Point Cloud Visualizations with 2DOF Input}, Volume = 18, Year = 2012

}

%

2011

@article{BE2011, Author = {Baake, M. and van~Enter, A.C.D.}, Journal = {J. Stat. Phys.}, Pages = {88--101}, Title = {Close-packed Dimers on the Line: Diffraction versus Dynamical Spectrum}, Volume = {143}, Year = {2011}, Number = {1}, URL = {http://dx.doi.org/10.1007/s10955-011-0163-5}, ABSTRACT = {The translation action of ℝ d on a translation bounded measure ω leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of ω, which is the carrier of the diffraction measure, lives on a subset of the dynamical spectrum. It is known that, under some mild assumptions, a pure point diffraction spectrum implies a pure point dynamical spectrum (the opposite implication always being true). For other systems, the diffraction spectrum can be a proper subset of the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with singular continuous diffraction) by van Enter and Miȩkisz (J. Stat. Phys. 66:1147–1153, 1992). Here, we construct a random system of close-packed dimers on the line that have some underlying long-range periodic order as well, and display the same type of phenomenon for a system with absolutely continuous spectrum. An interpretation in terms of ‘atomic’ versus ‘molecular’ spectrum suggests a way to come to a more general correspondence between these two types of spectra. } }

@article{BBEGH2011, Author = {Beersma, D.G.M. and Broer, H.W. and Efstathiou, K. and Gargar, K.A. and Hoveijn, I.}, Journal = {Physica D}, Pages = {1516--1527}, Volume = {19}, Title = {Pacer cell response to periodic Zeitgebers}, Year = {2011}, URL = {http://dx.doi.org/10.1016/j.physd.2011.06.019}, ABSTRACT = {Almost all organisms show some kind of time periodicity in their behavior. In mammals, the neurons of the suprachiasmatic nucleus form a biological clock regulating the activity-inactivity cycle of the animal. The main question is how this clock is able to entrain to the natural 24 h light-dark cycle by which it is stimulated. Such a system is usually modelled as a collection of mutually coupled 2-state (active-inactive) phase oscillators with an external stimulus (Zeitgeber). In this article however, we investigate the entrainment of a single pacer cell to the ensemble of other pacer cells. Moreover the stimulus of the ensemble is taken to be periodic. The pacer cell interacts with its environment by phase delay at the end of its activity interval and phase advance at the end of its inactivity interval. We develop a mathematical model for this system, naturally leading to a circle map depending on parameters like the intrinsic period and phase delay and advance. The existence of resonance tongues in a circle map shows that an individual pacer cell is able to synchronize with the ensemble. We furthermore show how the parameters in the model can be related to biological observable quantities. Finally we give several directions of further research.} }

@article{BDHS2011, Author = {Behrndt, J. and Derkach, V.A. and Hassi, S. and de~Snoo, H.S.V.}, Journal = {Operators and Matrices}, Pages = {679--706}, Title = {A realization theorem for generalized Nevanlinna pairs}, Volume = {5}, Year = {2011} }

@article{BHSW2011, Author = {Behrndt, J. and Hassi, S. and de~Snoo, H.S.V. and Wietsma, H.L.}, Journal = {Math. Nachr. (Editor's choice)}, Pages = {1334 – 1384}, Title = {Square-integrable solutions and Weyl functions for singular canonical systems}, Volume = {11}, Year = {2011} }

@article{BHSWW2011, Author = {Behrndt, J. and Hassi, S. and de~Snoo, H.S.V. and Wietsma, H.L. and Winkler, H.}, Journal = {Proc. Applied Math. Mech.}, Pages = {887--888}, Title = {Linear fractional transformations of Stieltjes functions}, Volume = {11}, Year = {2011} }

@article{BVBHV2011, title = {Exercise in Closed-Loop Control: A Major Hurdle}, author= {van~Bon, A.C. and Verbitskiy, E. and van~Basum, G. and Hoekstra, J.B.L. and De~Vries, J.H.},

journal = {Journal of Diabetes Science and Technology}, volume = {5}, number={6}, year= {2011}, pages={1337-1341}, }

@article{BrinkerKrishnamoorthiVerbitskiy2011,

author = {den~Brinker, A.C. and Krishnamoorthi, H. and Verbitskiy, E.A.}, title = {Similarities and Differences Between Warped Linear Prediction and Laguerre Linear Prediction}, journal = {IEEE Transactions on Audio, Speech & Language Processing}, volume = {19}, number = {1}, year = {2011}, pages = {24-33}, URL = {http://dx.doi.org/10.1109/TASL.2010.2042130}, bibsource = {DBLP, http://dblp.uni-trier.de}

}

@article{BDSSV2011, Author = {Broer, H. and Dijkstra, H. and Sim{\'o}, C. and Sterk, A. and Vitolo, R.}, Journal = {DCDS-B}, Pages = {73--102}, Title = {The dynamics of a low-order model for Atlantic Multidecadal Oscillation}, Volume = {16}, Number = {1}, Year = {2011}, URL = {http://dx.doi.org/10.3934/dcdsb.2011.16.73}, ABSTRACT = {Observational and model based studies provide ample evidence for the presence of multidecadal variability in the North Atlantic sea-surface temperature known as the Atlantic Multidecadal Oscillation (AMO). This variability is characterised by a multidecadal time scale, a westward propagation of temperature anomalies, and a phase difference between the anomalous meridional and zonal overturning circulations.

We study the AMO in a low-order model obtained by projecting a model for thermally driven ocean flows onto a 27-dimensional function space. We study bifurcations of attractors by varying the equator-to-pole temperature gradient () and a damping parameter (). For C and the low-order model has a stable equilibrium corresponding to a steady ocean flow. By increasing to 1 a supercritical Hopf bifurcation gives birth to a periodic attractor with the spatio-temporal signature of the AMO. Through a period doubling cascade this periodic orbit gives birth to Hénon-like strange attractors. Finally, we study the effects of annual modulation by introducing a time-periodic forcing. Then the AMO appears through a Hopf-Neĭmark-Sacker bifurcation. For C we detected at least 11 quasi-periodic doublings of the invariant torus. After these doublings we find quasi-periodic Hénon-like strange attractors.}

}

@BOOK{BroerTakens2011,

AUTHOR = {Broer, H.W. and Takens, F.}, TITLE = {Dynamical Systems and Chaos}, PUBLISHER = {Springer}, YEAR = {2011}, KEY = {testit}, URL = {http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-6869-2}, ABSTRACT = {Over the last four decades there has been extensive development in the theory of dynamical systems. This book starts from the phenomenological point of view reviewing examples. Hence the authors discuss oscillators, like the pendulum in many variation including damping and periodic forcing , the Van der Pol System, the Henon and Logistic families, the Newton algorithm seen as a dynamical system and the Lorenz and Rossler system are also discussed. The phenomena concern equilibrium, periodic, multi- or quasi-periodic and chaotic dynamic dynamics as these occur in all kinds of modeling and are met both in computer simulations and in experiments. The application areas vary from celestial mechanics and economical evolutions to population dynamics and climate variability. The book is aimed at a broad audience of students and researchers. The first four chapters have been used for an undergraduate course in Dynamical Systems and material from the last two chapters and from the appendices has been used for master and PhD courses by the authors. All chapters conclude with an exercise section. One of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory. Henk Broer and Floris Takens, professors at the Institute for Mathematics and Computer Science of the University of Groningen, are leaders in the field of dynamical systems. They have published a wealth of scientific papers and books in this area and both authors are members of the Royal Netherlands Academy of Arts and Sciences (KNAW).}

}

@article{BHVV2011, Author = {Broer, H. W. and Holtman, S. J. and Vegter, G. and Vitolo, R.}, Journal = {Regular and Chaotic Dynamics}, Pages = {39--50}, Title = {Dynamics and Geometry Near Resonant Bifurcations}, Volume = {16}, Year = {2011}, Number = {1-2}, URL = {http://dx.doi.org/10.1134/S1560354710520023}, ABSTRACT = {This paper provides an overview of the universal study of families of dynamical systems undergoing a Hopf-Neĭmarck-Sacker bifurcation as developed in [1–4]. The focus is on the local resonance set, i.e., regions in parameter space for which periodic dynamics occurs. A classification of the corresponding geometry is obtained by applying Poincaré-Takens reduction, Lyapunov-Schmidt reduction and contact-equivalence singularity theory, equivariant under an appropriate cyclic group. It is a classical result that the local geometry of these sets in the non-degenerate case is given by an Arnol’d resonance tongue. In a mildly degenerate situation a more complicated geometry given by a singular perturbation of a Whitney umbrella is encountered. Our approach also provides a skeleton for the local resonant Hopf-Neĭmarck-Sacker dynamics in the form of planar Poincaré-Takens vector fields. To illustrate our methods a leading example is used: A periodically forced generalized Duffing-Van der Pol oscillator. } }

@article{CifctciWaalkens2011, Author = {\c{C}ift\c{c}i, {\"U}. and Waalkens, H.}, Journal = {J. Phys. A}, Pages = {165202}, Title = {Holonomy reduced dynamics of triatomic molecules}, Volume = {44}, Year = {2011}, URL = {http://dx.doi.org/10.1088/1751-8113/44/16/165202}, ABSTRACT = {Whereas it is easy to reduce the translational symmetry of a molecular system using, e.g., Jacobi coordinates, the situation is much more involved for rotational symmetry. In this paper, we address the latter problem using holonomy reduction. We suggest that the configuration space may be considered as the reduced holonomy bundle with a connection induced by the mechanical connection. Using the fact that for the special case of the three-body problem the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than three bodies), we obtain a holonomy-reduced configuration space of topology R^3_+ x S^1. The dynamics then takes place on the cotangent bundle over the holonomy-reduced configuration space. On this phase space, there is an S1 symmetry action coming from the conserved reduced angular momentum which can be reduced using the standard symplectic reduction method. Using a theorem by Arnold it follows that the resulting symmetry-reduced phase space is again a natural mechanical phase space, i.e. a cotangent bundle. This is different from what is obtained from the usual approach where symplectic reduction is used from the outset. This difference is discussed in some detail, and a connection between the reduced dynamics of a triatomic molecule and the motion of a charged particle in a magnetic field is established. } }

@inproceedings{DettmannMorozovSieber2011,

AUTHOR = {Dettmann, C.P. and Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Microdisk resonators with two point scatterers}, BOOKTITLE = {ICTON: 2011 13th International Conference on Transparent Optical Networks}, PAGES = {1--3}, YEAR = {2011}, URL = {http://dx.doi.org/10.1109/ICTON.2011.5970933}, ABSTRACT = {Optical microdisk resonators exhibit modes with extremely high Q-factors. Their low lasing thresholds make circular microresonators good candidates for the realization of miniature laser sources. They have, however, the serious drawback that their light emission is isotropic, which is inconvenient for many applications. In our previous work, we showed that the presence of a point scatterer inside the disk can lead to highly directional modes in various frequency ranges while preserving the high Q-factors. In the present paper we generalize this idea to two point scatterers. The motivation for this work is that the strength of a point scatterer is difficult to control in experiments, and the presence of a second scatterer leads to a higher dimensional parameter space which permits to compensate this deficiency. Similar to the case of a single scatterer in a circular disk, the problem of finding the resonance modes in the presence of two scatterers is to a large extent analytically tractable.}

}

@article{EnterGroote2011, Author = {van~Enter, A.C.D. and de~Groote, E.}, Journal = {J. Stat. Phys.}, Pages = {223--228}, Title = {An Ultrametric State Space with a Dense Discrete Overlap Distribution: Paperfolding Sequences}, Volume = {142}, Year = {2011}, URL = {http://dx.doi.org/10.1007/s10955-010-0107-5}, ABSTRACT = {We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support (as a closed set) is the full interval [−1,+1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models. } }

@article{EnterIacobelliTaati2011, Author = {van~Enter, A.C.D. and Iacobelli, G. and Taati, S.}, Journal = {Prog. Theor. Phys.}, Pages = {983--991}, Title = {First-Order Transition in Potts Models with “Invisible” States -- Rigorous Proofs --}, Volume = {126}, Year = {2011}, URL = {http://dx.doi.org/10.1143/PTP.126.983}, ABSTRACT = {In some recent papers by Tamura, Tanaka and Kawashima [R. Tamura, S. Tanaka and N. Kawashima, Prog. Theor. Phys. 124 (2010), 381; S. Tanaka, R. Tamura and N. Kawashima, J. Phys.: Conf. Ser. 297 (2011), 012022; S. Tanaka and R. Tamura, arXiv:1012.4254] a class of Potts models with “invisible” states was introduced, for which the authors argued, by numerical arguments and by a mean-field analysis, that a first-order transition occurs. Here we show that the existence of this first-order transition can be proven rigorously, by relatively minor adaptations of existing proofs for ordinary Potts models. In our argument, we present a random-cluster representation for the model, which might also be of interest for general parameter values of the model. } }

@article{EnterKuelskeOpoku2011, Author = {van~Enter, A.C.D. and K{\"u}lske, C. and Opoku, A.}, Journal = {J. Phys. A: Math. Theor.}, Pages = {475002}, Title = {Discrete approximations to vector spin models}, Volume = {44}, Year = {2011}, URL = {http://dx.doi.org/10.1088/1751-8113/44/47/475002}, ABSTRACT = {We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. } }

@article{EnterRomanoZagrebnov2011, Author = {van~Enter, A.C.D. and Romano, S. and Zagrebnov, V.A.}, Journal = {J. Phys. A}, Pages = {208001}, Title = {Comment on 'Phase transition of a two-dimensional generalized XY model'}, Volume = {44}, Year = {2011}, URL = {http://dx.doi.org/10.1088/1751-8113/44/20/208001}, ABSTRACT = {We point out that the claim of strong universality of the paper by Komura and Okabe (2011 J. Phys. A: Math. Theor. 44 015002) is incorrect, as it contradicts known rigorous results.} }

@PHDTHESIS{Ermolaev2011,

AUTHOR = {Ermolaev, Victor N.}, TITLE = {Gibbsian properties: examples of failures and an application}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {September}, YEAR = {2011}, NOTE = {Advisors: C. K{\"u}lske, A.C.D. van Enter and E.A. Verbitskiy, 127 pages}, URL = {http://irs.ub.rug.nl/ppn/337152624}

}

@PHDTHESIS{Fleurke2011,

AUTHOR = {Fleurke, Sjoert R.}, TITLE = {Stochastic models for particle deposition, car parking and frequency assignment}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {March}, YEAR = {2011}, NOTE = {Advisors: C. K{\"u}lske, H.G. Dehling (IMAU) and A.C.D. van Enter, 146 pages}, URL = {http://irs.ub.rug.nl/ppn/333030966}

}

@article{HSW2011, Author = {Hales, R. and Sieber, M. and Waalkens, H.}, Journal = {J. Phys. A}, Pages = {155305}, Title = {Trace formula for a dielectric microdisk with a point scatterer}, Volume = {44}, Year = {2011}, URL = {http://dx.doi.org/10.1088/1751-8113/44/15/155305}, ABSTRACT = {Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In this paper, we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions. } }

@article{HVRSB2011, Author = {Holland, M. P. and Vitolo, R. and Rabassa, P. and Sterk, A. E. and Broer, H. W.}, Journal = {Physica D}, Pages = {154--184}, Title = {Extreme value laws in dynamical systems under physical observables}, Volume = { }, Number = { }, Year = {2011}, URL = {http://dx.doi.org/10.1016/j.physd.2011.11.005}, Abstract = {Extreme value theory for chaotic deterministic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block

maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs statistical inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observations along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system's invariant measure. However, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not functions of the distance from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable's level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (H\'enon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws.}

}

@article {SchmidtVerbitskiy2011,

AUTHOR = {Schmidt, Klaus and Verbitskiy, Evgeny}, TITLE = {New directions in algebraic dynamical systems}, JOURNAL = {Regul. Chaotic Dyn.}, FJOURNAL = {Regular and Chaotic Dynamics. International Scientific Journal}, VOLUME = {16}, YEAR = {2011}, NUMBER = {1-2}, PAGES = {79--89}, ISSN = {1560-3547}, MRCLASS = {37Axx (28D20 31C05 37Nxx 82B23)}, MRNUMBER = {2774380}, DOI = {10.1134/S1560354710520072}, URL = {http://dx.doi.org/10.1134/S1560354710520072},

}

@article {SOVS2011,

AUTHOR = { Škorić, B. and Obi, C. and Verbitskiy, E.A. and Schoenmakers, B.}, TITLE = {Sharp lower bounds on the extractable randomness from non-uniform sources}, JOURNAL = {Inform. and Comput.}, FJOURNAL = {Information and Computation}, VOLUME = {209}, YEAR = {2011}, NUMBER = {8}, PAGES = {1184--1196}, ISSN = {0890-5401}, MRCLASS = {94A60 (68Q87 94A17)}, MRNUMBER = {2850662},

}

@article{SnooWinklerWojtylak2011, Author = {de~Snoo, H.S.V. and Winkler, H. and Wojtylak, M.}, Journal = {J. Math. Anal. Appl.}, Pages = {399--417}, Title = {Zeros of nonpositive type of generalized Nevanlinna functions with one negative square}, Volume = {382}, Year = {2011}, }

@article{Verbitskiy2011, author = {Verbitskiy, E.A.},

title = {Thermodynamics of Hidden Markov Processes}, pages = {258-272}, note={Papers from the Banff International Research Station Workshop on Entropy of Hidden Markov Processes and Connections to Dynamical Systems}, journal= {London Mathematical Society, Lecture Note Series \textbf{385} B. Markus, K. Petersen, T. Weissman, (Eds)}, year= {2011}, }

@article{Verbitskiy2011b, title = {On factors of -measures}, journal = {Indagationes Mathematicae}, volume = {22}, number = {3-4}, pages = {315 - 329}, year = {2011}, note = {Devoted to: Floris Takens (1940-2010)}, issn = {0019-3577}, URL = {http://dx.doi.org/10.1016/j.indag.2011.09.001}, url = "http://www.sciencedirect.com/science/article/pii/S0019357711000437", author = {Verbitskiy, E.A.} }

@article{VitoloBroerSimo2011, Author = {Vitolo, R. and Broer, H. and Sim{\'o}, C.}, Journal = {Regular and Chaotic Dynamics}, Pages = {154--184}, Title = {Quasi-periodic Bifurcations of Invariant Circles in Low-dimensional Dissipative Dynamical Systems}, Volume = {16}, Number = {1-2}, Year = {2011}, URL = {http://dx.doi.org/10.1134/S1560354711010060}, Abstract = {This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.} }

%

2010

@article{AssematEfstathiouJoyeuxSugny2010, Author = {Ass{\'e}mat, E. and Efstathiou, K. and Joyeux, M. and Sugny, D.}, Journal = {Phys. Rev. Lett.}, Number = {11}, Pages = {113002}, Title = {Fractional bidromy in the vibrational spectrum of {HOCl}}, Volume = {104}, Year = {2010}, URL = {http://dx.doi.org/10.1103/PhysRevLett.104.113002}, ABSTRACT = {We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative example to show the presence of nontrivial fractional bidromy. To our knowledge, this is the first example of a molecular system where such a generalized monodromy is exhibited. } }

@article {BehrndtHassiSnooWietsma2010,

AUTHOR = {Behrndt, J. and Hassi, S. and de~Snoo, H.S.V. and Wietsma, R.}, TITLE = {Monotone convergence theorems for semibounded operators and forms with applications}, JOURNAL = {Proc. Royal Soc. Edinburgh, Sec. A}, VOLUME = {140}, NUMBER = {5}, YEAR = {2010}, PAGES = {927--951}, URL = {http://dx.doi.org/10.1017/S030821050900078X},

ABSTRACT = {Let Hn be a monotone sequence of non-negative self-adjoint operators or relations in a Hilbert space. Then there exists a self-adjoint relation Hinfty such that Hn converges to Hinfty in the strong resolvent sense. This result and related limit results are explored in detail and new simple proofs are presented. The corresponding statements for monotone sequences of semi-bounded closed forms are established as immediate consequences. Applications and examples, illustrating the general results, include sequences of multiplication operators, Sturm–Liouville operators with increasing potentials, forms associated with Krein–Feller differential operators, singular perturbations of non-negative self-adjoint operators and the characterization of the Friedrichs and Krein–von Neumann extensions of a non-negative operator or relation.} }

@article {BonckaertHoveijnVerstringe2010,

AUTHOR = {Bonckaert, P. and Hoveijn, I. and Verstringe, F.}, TITLE = {Local analytic reduction of

families of diffeomorphisms},

JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {367}, YEAR = {2010}, NUMBER = {1}, PAGES = {317--328}, URL = {http://dx.doi.org/10.1016/j.jmaa.2010.01.032}, ABSTRACT={We study local analytic simplification of families of analytic maps near a hyperbolic fixed point. A particularly important application of the main result concerns families of hyperbolic saddles, where Siegel's theorem is too fragile, at least in the analytic category. By relaxing on the formal normal form we obtain analytic conjugacies. Since we consider families, it is more convenient to state some results for analytic maps on a Banach space; this gives no extra complications. As an example we treat a family passing through a 1:−1 resonant saddle.}

}

@article {Broer2010,

AUTHOR = {Broer, H.W.}, TITLE = {Do Diophantine vectors form a Cantor bouquet?}, JOURNAL = {Journ. Difference Equations and Applications}, VOLUME = {16}, YEAR = {2010}, NUMBER = {5/6}, PAGES = {433--434}, URL = {http://dx.doi.org/10.1080/10236190903203853}, ABSTRACT={We introduce the set of Diophantine vectors in R^n, which is a standard notion in KAM Theory. The problem is whether this set forms a Cantor bouquet.}

}

@article {BroerEfstathiouLukina2010,

AUTHOR = {Broer, H. W. and Efstathiou, K. and Lukina, O. V.}, TITLE = {A geometric fractional monodromy}, JOURNAL = {DCDS-S}, VOLUME = {3}, YEAR = {2010}, NUMBER = {4}, PAGES = {517--532}, URL = {http://aimsciences.org/journals/displayArticles.jsp?paperID=5455}, ABSTRACT={We prove the existence of fractional monodromy for two degree of freedom integrable Hamiltonian systems with one-parameter families of curled tori under certain general conditions. We describe the action coordinates of such systems near curled tori and we show how to compute fractional monodromy using the notion of the rotation number.}

}

@article {BroerGaiko2010,

AUTHOR = {Broer, H. W. and Gaiko, V. A.}, TITLE = {Global qualitative analysis of a quartic ecological model}, JOURNAL = {Nonlinear Anal.}, VOLUME = {72}, YEAR = {2010}, NUMBER = {2}, PAGES = {628--634}, URL = {http://dx.doi.org/10.1016/j.na.2009.07.004}, ABSTRACT={In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit cycles.}

}

@article {BroerHanssmannSevryuk2010,

AUTHOR = {Broer, H. W. and Han{\ss}mann, H. and Sevryuk (eds.), M. B. }, TITLE = {Special Issue on KAM Theory and its applications.}, JOURNAL = {DCDS-S}, VOLUME = {3}, YEAR = {2010}, NUMBER = {4}, URL = {http://aimsciences.org/journals/displayArticles.jsp?paperID=5454}, ABSTRACT={This issue of Discrete and Continuous Dynamical Systems, Series S, is a collection of papers in the area of KAM theory and its applications. KAM theory, named after its founders A.N. Kolmogorov [1, 2], V.I. Arnol'd [3, 4, 5], and J.K. Moser [6, 7], is a major part of Dynamical Systems Theory and Qualitative Theory of Differential Equations, both ordinary and partial (the descriptive term "KAM theory" was coined in a 1968 Russian preprint by F.M. Izrailev and B.V. Chirikov). It studies the typical occurrence of quasi-periodicity in non-integrable dynamical systems and is often regarded as one of the foremost branches of modern Nonlinear Dynamics.}

}

@BOOK{BroerHasselblattTakens2010,

AUTHOR = {Broer, H.W. and Haselblatt, B. and Takens (eds.), F.}, TITLE = {Handbook of Dynamical Systems, Vol. 3}, PUBLISHER = {North-Holland}, YEAR = {2010}, URL = {http://www.elsevierdirect.com/ISBN/9780444531414/Handbook-of-Dynamical-Systems}, ABSTRACT = {In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.}

}

@article {BroerHoltmanVegter2010,

AUTHOR = {Broer, H. W. and Holtman, S.J. and Vegter, G.}, TITLE = {Recognition of resonance type in periodically forced oscillators}, JOURNAL = {Physica D}, VOLUME = {239}, YEAR = {2010}, NUMBER = {17}, PAGES = {1627--1636}

}

@inproceedings{BroerSevryuk2010,

AUTHOR = {Broer, H.W. and Sevryuk, M.B.}, TITLE = {KAM Theory: quasi-periodicity in dynamical systems}, BOOKTITLE = {Handbook of Dynamical Systems}, VOLUME = {3}, PUBLISHER = {North-Holland},

Editor = {Broer, H.W. and Hasselblatt, B. and Takens, F.},

YEAR = {2010}, PAGES = {249--344}, URL = {http://www.elsevierdirect.com/ISBN/9780444531414/Handbook-of-Dynamical-Systems}

}

@article {BroerSimoVitolo2010,

AUTHOR = {Broer, H. W. and Sim{\'o}, C. and Vitolo, R.}, TITLE = {Chaos and quasi-periodicity in diffeomorphisms of the solid torus}, JOURNAL = {DCDS-B}, VOLUME = {14}, YEAR = {2010}, NUMBER = {3}, PAGES = {871--905}, URL = {http://dx.doi.org/10.3934/dcdsb.2010.14.871}, ABSTRACT ={This paper focuses on the parametric abundance and the 'Cantorial' persistence under perturbations of a recently discovered class of strange attractors for diffeomorphisms, the so-called quasi-periodic Hénon-like. Such attractors were first detected in the Poincaré map of a periodically driven model of the atmospheric flow: they were characterised by marked quasi-periodic intermittency and by , where and are the two largest Lyapunov exponents. It was also conjectured that these attractors coincide with the closure of the unstable manifold of a hyperbolic invariant circle of saddle-type. This type of attractor is here investigated in a model map of the solid torus, constructed by a skew coupling of the Hénon family of planar maps with the Arnold family of circle maps. It is proved that Hénon-like strange attractors occur in certain parameter domains. Numerical evidence is produced, suggesting that quasi-periodic circle attractors and quasi-periodic Hénon-like attractors persist in relatively large subsets of the parameter space. We also discuss two problems in the numerical identification of so-called strange nonchaotic attractors and the persistence of all these classes of attractors under perturbation of the skew product structure.}

}

@inproceedings{BroerTakens2010,

AUTHOR = {Broer, H.W. and Takens, F.}, TITLE = {Preliminaries in Dynamical Systems Theory}, BOOKTITLE = {Handbook of Dynamical Systems}, PUBLISHER = {North-Holland},

Editor = {Broer, H.W. and Hasselblatt, B. and Takens, F.},

VOLUME = {3}, YEAR = {2010}, PAGES = {1--42}, URL = {http://www.elsevierdirect.com/ISBN/9780444531414/Handbook-of-Dynamical-Systems}

}

@article{EfstathiouSadovskii2010, Author = {Efstathiou, K. and Sadovski{\'i}, D. A.}, Journal = {Rev. Mod. Phys.}, Number = {3}, Pages = {2099-2154}, Title = {Normalization and global analysis of perturbations of the hydrogen atom}, Volume = {82}, Year = {2010}, URL = {http://dx.doi.org/10.1103/RevModPhys.82.2099}, ABSTRACT = {The hydrogen atom perturbed by sufficiently small homogeneous static electric and magnetic fields of arbitrary mutual alignment is a specific perturbation of the Kepler system with three degrees of freedom and three parameters. Normalization of the Keplerian symmetry reveals that the parameter space is stratified into resonant zones of systems, each zone with an internal dynamical stratification of its own (Efstathiou, Sadovskií, and Zhilinskií, 2007, Proc. R. Soc. London, Ser. A 463, 1771). Based on the fully integrable approximation, the bundle of invariant tori of individual systems within zones is characterized globally and the qualitative dynamical stratification is uncovered. The techniques involved in this analysis are illustrated with the example of the 1:1 resonance zone (near orthogonal fields) whose structure is known at present. Applications in the corresponding quantum system are also described.} }

@article{EfstathiouSugnyt2010, Author = {Efstathiou, K. and Sugny, D.}, Journal = {J. Phys. A}, Number = {8}, Pages = {085216}, Title = {Integrable Hamiltonian systems with swallowtails}, Volume = {43}, Year = {2010}, URL = {http://dx.doi.org/10.1088/1751-8113/43/8/085216}, ABSTRACT = {We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovskií and Zhilinskií (2007 Ann. Phys. 322 164–200) is discussed. } }

@MISC {Enter2010,

AUTHOR = {van Enter, A.C.D.}, TITLE = {Gemiste Nobelprijzen}, HOWPUBLISHED = {Nederlands Tijdschrift voor Natuurkunde, vol. 76, p. 90}, YEAR = {2010},

}

@MISC {Enter2010b,

AUTHOR = {van Enter, A.C.D.}, TITLE = {Waar doen we het voor (Editorial) }, JHOWPUBLISHED = {Nederlands Tijdschrift voor Natuurkunde, vol. 76, p. 95}, YEAR = {2010},

}

@MISC {Enter2010c,

AUTHOR = {van Enter, A.C.D.}, TITLE = {Waarom volgens mij de 1e geldstroom relatief wel zou moeten groeien}, HOWPUBLISHED = {Nederlands Tijdschrift voor Natuurkunde, vol. 76, p. 381}, YEAR = {2010},

}

@article {EnterFernandezHollanderRedig2010,

AUTHOR = {van Enter, A.C.D. and Fernandez, R. and den~Hollander, F. and Redig, F.}, TITLE = {A Large-Deviation View on Dynamical Gibbs-non-Gibbs Transitions}, JOURNAL = {Mosc. Math. J.}, VOLUME = {10}, NUMBER = {4}, YEAR = {2010}, PAGES = {687--711}, URL = {http://www.ams.org/journals/distribution/mmj/vol10-4-2010/abst10-4-2010.html#van-enter-etal}, ABSTRACT = {We develop a space-time large-deviation point of view on Gibbs-non-Gibbs transitions in spin systems subject to a stochastic spin-flip dynamics. Using the general theory for large deviations of functionals of Markov processes outlined in a recent book by Feng and Kurtz, we show that the trajectory under the spin-flip dynamics of the empirical measure of the spins in a large block in $Z^\d$ satisfies a large deviation principle in the limit as the block size tends to innity. The associated rate function can be computed as the action functional of a Lagrangian that is the Legendre transform of a certain non-linear generator, playing a role analogous to the moment-generating function in the G{\"a}rtner-Ellis theorem of large deviation theory when this is applied to finite-dimensional Markov processes. This rate function is used to dene the notion of "bad empirical measures", which are the discontinuity points of the optimal trajectories (i.e., the trajectories minimizing the rate function) given the empirical measure at the end of the trajectory. The dynamical Gibbs-non-Gibbs transitions are linked to the occurrence of bad empirical measures: for short times no bad empirical measures occur, while for intermediate and large times bad empirical measures are possible. A future research program is proposed to classify the various possible scenarios behind this crossover, which we refer to as a "nature-versus-nurture" transition.}

}

@article {EnterKuelskeOpokuRuszel2010,

AUTHOR = {van Enter, A.C.D. and K{\"u}lske, C. and Opoku, A.A. and Ruszel, W.M.}, TITLE = {Gibbs–non-Gibbs properties for n-vector lattice and mean-field models}, JOURNAL = {Braz. J. Prob. Stat.}, VOLUME = {24}, YEAR = {2010}, NUMBER = {2}, PAGES = {226--255}, URL = {http://dx.doi.org/10.1214/09-BJPS029}, ABSTRACT={We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.}

}

@article {EnterVerbitskiy2010,

AUTHOR = {van Enter, A.C.D. and Verbitskiy, E.}, TITLE = {Erasure Entropies and Gibbs Measures}, JOURNAL = {Markov Processes Relat. Fields}, VOLUME = {16}, YEAR = {2010}, PAGES = {3--14}, ABSTRACT={Recently Verdu and Weissman introduced erasure entropies, which are meant to measure the information carried by one or more symbols given all of the remaining symbols in the realization of a random process or field. A natural relation to Gibbs measures has also been observed. In this short note we study this relation further, review a few earlier contributions from statistical mechanics, and provide the formula for the erasure entropy of a Gibbs measure in terms of the corresponding potential. For some 2-dimensional Ising models, for which Verdu and Weissman suggested a numerical procedure, we show how to obtain an exact formula for the erasure entropy.}

}

@article {FleigeHassideSnooWinkler2010,

AUTHOR = {Fleige, A. and Hassi, S. and de~Snoo, H.S.V. and Winkler, H.}, TITLE = {Sesquilinear forms corresponding to a non-semibounded

{S}turm-{L}iouville operator},

JOURNAL = {Proc. Royal Soc. Edinburgh.}, VOLUME = {140A}, YEAR = {2010}, PAGES = {291--318}

}

@inproceedings{GoussevSchubertWaalkensWiggins2010,

AUTHOR = {Goussev, A. and Schubert, R. and Waalkens, H. and Wiggins, S.}, TITLE = {Quantum Theory of Reactive Scattering in Phase Space}, BOOKTITLE = {Advances in Quantum Chemistry}, VOLUME = {60}, YEAR = {2010}, PAGES = {269--332}, URL = {http://www.elsevier.com/wps/find/bookdescription.cws_home/720862/description#description}

}

@inproceedings{GoussevSchubertWaalkensWiggins2010b,

AUTHOR = {Goussev, A. and Schubert, R. and Waalkens, H. and Wiggins, S.}, TITLE = {A Periodic Orbit Formula for Quantum Reactions Through Transition States}, BOOKTITLE = {AIP Conf. Proc.}, VOLUME = {1281}, YEAR = {2010}, PAGES = {1593--1596}, URL = {http://link.aip.org/link/?APCPCS/1281/1593/1}, ABSTRACT = {Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.}

}

@article{GoussevSchubertWaalkensWiggins2010c,

AUTHOR = {Goussev, A. and Schubert, R. and Waalkens, H. and Wiggins, S.}, TITLE = {The flux-flux correlation function for anharmonic barriers}, JOURNAL = {J. Chem. Phys.}, VOLUME = {133}, YEAR = {2010}, PAGES = {244113}, URL = {http://dx.doi.org/10.1063/1.3518425},

ABSTRACT = {The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that for a general f degree-of-freedom system having an index one saddle the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one-dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.} }

@INCOLLECTION{LindSchmidtVerbitskiy2010,

```
AUTHOR = {Lind, D. and Schmidt, K. and Verbitskiy, E.},
TITLE = {Entropy and growth rate of periodic points of algebraic $\mathbb Z^d$-actions},
EDITOR = {Sergiy Kolyada, Yuri Manin, Martin M{\"o}ller and Pieter Moree
```

\&Thomas Warda},

BOOKTITLE = {Contemporary Mathematics}, PUBLISHER = {Amer. Math. Society}, ADDRESS = {US}, VOLUME = {532}, PAGES = {195--211}, YEAR = {2010}, URL = {http://ams.org/bookstore?fn=20&arg1=diffequ&ikey=CONM-532}, ABSTRACT = {Expansive algebraic Z d-actions corresponding to ideals are characterized by the property that the complex variety of the ideal is disjoint from the multiplicative unit torus. For such actions it is known that the limit for the growth rate of periodic points exists and equals the entropy of the action. We extend this result to actions for which the complex variety intersects the multiplicative torus in a finite set. The main technical tool is the use of homoclinic points which decay rapidly enough to be summable.}

}

@PHDTHESIS{Hales2010,

AUTHOR = {Hales, Robert F. M.}, TITLE = {Two Applications of Semiclassical Techniques to Open Systems: Transition State Theory and Microcavity Lasers}, SCHOOL = {University of Bristol}, TYPE = {PhD Dissertation}, ADDRESS = {School of Mathematics}, MONTH = {July}, YEAR = {2010}, NOTE = {Advisor: H. Waalkens, 163 pages},

}

@article {HoekstraVogelzangVerbitskiyNijsten2010,

AUTHOR = {Hoekstra, M. and Vogelzang, M. and Verbitskiy, E. and Nijsten, M.W.N.}, TITLE = {Hourly measurements not required for safe and effective glycemic control in the critically ill patient}, JOURNAL = {Critical Care}, VOLUME = {14}, YEAR = {2010}, NUMBER = {404}, URL = {http://dx.doi.org/10.1186/cc8190 }

}

@article {HoveijnKirillov2010,

AUTHOR = {Hoveijn, I. and Kirillov, O.N.}, TITLE = {Singularities on the boundary of the stability domain near 1:1 resonance}, JOURNAL = {J. Diff. Equ.}, VOLUME = {248}, YEAR = {2010}, NUMBER = {10}, PAGES = {2585--2670}, URL = {http://dx.doi.org/10.1016/j.jde.2009.12.004 }, ABSTRACT={We study the linear differential equation in 1:1-resonance. That is, x in R^4 and L is 4×4 matrix with a semi-simple double pair of imaginary eigenvalues (iβ,−iβ,iβ,−iβ). We wish to find all perturbations of this linear system such that the perturbed system is stable. Since linear differential equations are in one-to-one correspondence with linear maps we translate this problem to gl(4,R). In this setting our aim is to determine the stability domain and the singularities of its boundary. The dimension of is 16, therefore we first reduce the dimension as far as possible. Here we use a versal unfolding of L, i.e. a transverse section of the orbit of L under the adjoint action of GL(4,R). Repeating a similar procedure in the versal unfolding we are able to reduce the dimension to 4. A 3-sphere in this 4-dimensional space contains all information about the neighborhood of L in gl(4,R). Considering the 3-sphere as two 3-discs glued smoothly along their common boundary we find that the boundary of the stability domain is contained in two right conoids, one in each 3-disc. The singularities of this surface are transverse self-intersections, Whitney umbrellas and an intersection of self-intersections where the surface has a self-tangency. A Whitney stratification of the 3-sphere such that the eigenvalue configurations of corresponding matrices are constant on strata allows us to describe the neighborhood of L and in particular identify the stability domain.}

}

@article {LabrousseSandoviciSnooWinkler2010,

AUTHOR = {Labrousse, J.-Ph. and Sandovici, A. and de~Snoo, H.S.V. and Winkler, H.}, TITLE = {The {K}ato decomposition of quasi-{F}redholm relations}, JOURNAL = {Operators and Matrices}, VOLUME = {4}, YEAR = {2010}, PAGES = {1--51}

}

@article {RedigRoellyRuszel2010,

AUTHOR = {Redig, F. and Roelly, S. and Ruszel, W.}, TITLE = {Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction}, JOURNAL = {J. Stat. Phys.}, VOLUME = {138}, YEAR = {2010}, NUMBER = {6}, PAGES = {1124--1144}, URL = {http://dx.doi.org/10.1007/s10955-010-9926-7}, ABSTRACT={We consider a class of infinite-dimensional diffusions where the interaction between the components has a finite extent both in space and time. We start the system from a Gibbs measure with a finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t 0>0 such that the distribution at time t≤t 0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.}

}

@PHDTHESIS{Ruszel2010,

AUTHOR = {Ruszel, Wioletta M.}, TITLE = {Gibbs and non-Gibbs aspects of continuous spin models}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {September}, YEAR = {2010}, NOTE = {Advisors: A.C.D. van Enter and C. K{\"u}lske (Ruhr-Universit{\"a}t Bochum), 169 pages}, URL = {http://dissertations.ub.rug.nl/faculties/science/2010/w.m.ruszel}

}

@article {SchmidtVertskiy2010,

AUTHOR = {Schmidt, K. and Verbitskiy, E.}, TITLE = {New directions in algebraic dynamical systems}, JOURNAL = {Regular and Chaotic Dynamics}, YEAR = {2010}, URL = {http://link.aps.org/doi/10.1134/S1560354710520072}, ABSTRACT={The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.}

}

@article {SchubertWaalkensGoussevWiggins2010,

AUTHOR = {Schubert, R. and Waalkens, H. and Goussev, A. and Wiggins, S.}, TITLE = {Periodic-orbit formula for quantum reactions through transition states}, JOURNAL = {Phys. Rev. A}, VOLUME = {82}, YEAR = {2010}, NUMBER = {1}, PAGES = {012707}, URL = {http://link.aps.org/doi/10.1103/PhysRevA.82.012707}, ABSTRACT={Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.}

}

@PHDTHESIS{Sterk2010,

AUTHOR = {Sterk, Alef E.}, TITLE = {Atmospheric variability and the Atlantic Multidecadal Oscillation. Mathematical Analysis of Reduced Models}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {October}, YEAR = {2010}, NOTE = {Advisors: H.W. Broer, H.A. Dijkstra (IMAU) and C. Sim{\'o} (University of Barcelona), 119 pages}, URL = {http://irs.ub.rug.nl./ppn/328983845}

}

@article {SterkVitoloBroerSimoDijkstra2010,

AUTHOR = {Sterk, A.E. and Vitolo, R. and Broer, H.W. and , Sim{\'o}, C. and Dijkstra, H.A.}, TITLE = {New nonlinear mechanisms of midlatitude atmospheric low-frequency variability}, JOURNAL = {Physica D}, VOLUME = {239}, YEAR = {2010}, NUMBER = {10}, PAGES = {702--718}, URL = {http://dx.doi.org/0.1016/j.physd.2010.02.003}, ABSTRACT={This paper studies the dynamical mechanisms potentially involved in the so-called atmospheric low-frequency variability, occurring at midlatitudes in the Northern Hemisphere. This phenomenon is characterised by recurrent non-propagating and temporally persistent flow patterns, with typical spatial and temporal scales of 6000–10 000 km and 10–50 days, respectively.

We study a low-order model derived from the 2-layer shallow-water equations on a β-plane channel. The main ingredients of the low-order model are a zonal flow, a planetary scale wave, orography, and a baroclinic-like forcing. A systematic analysis of the dynamics of the low-order model is performed using techniques and concepts from dynamical systems theory. Orography height (h0) and magnitude of zonal wind forcing (U0) are used as control parameters to study the bifurcations of equilibria and periodic orbits. Along two curves of Hopf bifurcations an equilibrium loses stability () and gives birth to two distinct families of periodic orbits. These periodic orbits bifurcate into strange attractors along three routes to chaos: period doubling cascades, breakdown of 2-tori by homo- and heteroclinic bifurcations, or intermittency ( and ). The observed attractors exhibit spatial and temporal low-frequency patterns comparing well with those observed in the atmosphere. For the periodic orbits have a period of about 10 days and patterns in the vorticity field propagate eastward. For , the period is longer (30–60 days) and patterns in the vorticity field are non-propagating. The dynamics on the strange attractors are associated with low-frequency variability: the vorticity fields show weakening and strengthening of non-propagating planetary waves on time scales of 10–200 days. The spatio-temporal characteristics are “inherited” (by intermittency) from the two families of periodic orbits and are detected in a relatively large region of the parameter plane. This scenario provides a characterisation of low-frequency variability in terms of intermittency due to bifurcations of waves.} }

@INCOLLECTION{Verbitskiy2010,

AUTHOR = {Verbitskiy, E.}, TITLE = {Mathematics in the industrial environment: Dutch

perspective},

EDITOR = {G.~van~Dijk and M.~Wakayama}, BOOKTITLE = {Casimir Force, Casimir Operators and the Riemann Hypothesis}, PUBLISHER = {de~Gruyter}, ADDRESS = {Berlin}, PAGES = {21--28}, YEAR = {2010}, URL = {http://gcoe-mi.jp/english/activity/ac_inner/id:11}, ABSTRACT = {After a short historic overview, I will discuss "best practices" of applied mathematics in industrial environments. I will also discuss approaches to training students in industrial mathematics used in the Netherlands.}

}

@article {Verbitskiy2010b,

AUTHOR = {Verbitskiy, E.}, TITLE = {Variational Principle for Fuzzy Gibbs Measures}, JOURNAL = {Moscow Mathematical Journal}, VOLUME = {10}, NUMBER = {4}, YEAR = {2010}, PAGES = {811--829}, URL = {http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000284154300009}, ABSTRACT={In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memory-less channels in information theory, continuous block factors of symbolic dynamical systems, and many renormalization transformations of statistical mechanics. The main result is the generalization of the classical variational principle of Dobrushin-Lanford-Ruelle for Gibbs measures to the class of fuzzy Gibbs measures.}

}

@article {VerbitskiyTuylsObiSkoricSchoenmaker2010,

AUTHOR = {Verbitskiy, E. and Tuyls, P. and Obi, C. and Skoric, B. and Schoenmakers, B.}, TITLE = {Key Extraction From General Non-Discrete Signals}, JOURNAL = {EEE Trans. on Information Forensics and Security}, VOLUME = {5}, NUMBER = {2}, YEAR = {2010}, PAGES = {269--279}, URL = {http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=05439855}, ABSTRACT={We address the problem of designing optimal schemes for the generation of secure cryptographic keys from continuous noisy data. We argue that, contrary to the discrete case, a universal fuzzy extractor does not exist. This implies that in the continuous case, key extraction schemes have to be designed for particular probability distributions. We extend the known definitions of the correctness and security properties of fuzzy extractors. Our defi- nitions apply to continuous as well as discrete variables. We pro- pose a generic construction for fuzzy extractors from noisy contin- uous sources, using independent partitions. The extra freedom in the choice of discretization, which does not exist in the discrete case, is advantageously used to give the extracted key a uniform distribu- tion. We analyze the privacy properties of the scheme and the error probabilities in a one-dimensional toy model with simplified noise. Finally, we study the security implications of incomplete knowl- edge of the source’s probability distribution P. We derive a bound on the min-entropy of the extracted key under the worst-case as- sumption, where the attacker knows P. exactly.}

}

@article {VitoloBroerSimo2010,

AUTHOR = {Vitolo, R. and Broer, H.W. and Sim{\'o}, C.}, TITLE = {Routes to chaos in the Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms}, JOURNAL = {Nonlinearity}, VOLUME = {23}, YEAR = {2010}, PAGES = {1919--1947}, URL = {http://dx.doi.org/10.1088/0951-7715/23/8/007}, ABSTRACT={Dynamical phenomena are studied near a Hopf-saddle-node bifurcation of fixed points of 3D-diffeomorphisms. The interest lies in the neighbourhood of weak resonances of the complex conjugate eigenvalues. The 1 : 5 case is chosen here because it has the lowest order among the weak resonances, and therefore it is likely to have a most visible influence on the bifurcation diagram. A model map is obtained by a natural construction, through perturbation of the flow of a Poincaré–Takens normal form vector field. Global bifurcations arise in connection with a pair of saddle-focus fixed points: homoclinic tangencies occur near a sphere-like heteroclinic structure formed by the 2D stable and unstable manifolds of the saddle points. Strange attractors occur for nearby parameter values and three routes are described. One route involves a sequence of quasi-periodic period doublings of an invariant circle where loss of reducibility also takes place during the process. A second route involves intermittency due to a quasi-periodic saddle-node bifurcation of an invariant circle. Finally a route involving heteroclinic phenomena is discussed. Multistability occurs in several parameter subdomains: we analyse the structure of the basins for a case of coexistence of a strange and a quasi-periodic attractor and for coexistence of two strange attractors. By construction, the phenomenology of the model map is expected in generic families of 3D diffeomorphisms.}

}

@article {WaalkensWiggins2010,

AUTHOR = {Waalkens, H. and Wiggins, S.}, TITLE = {Geometric Models of the Phase Space Structures Governing Reaction Dynamics}, JOURNAL = {Reg. Chaot. Dyn.}, VOLUME = {15}, YEAR = {2010}, PAGES = {1--39}, URL = {http://dx.doi.org/10.1134/S1560354710010016}, ABSTRACT={Hamiltonian dynamical systems possessing equilibria of saddle ? center ? ... ? center stability type display reaction-type dynamics for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow bottlenecks created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description of the phase space structures that are responsible for controlling transport in these problems. Of central importance is the existence of a Normally Hyperbolic Invariant Manifold (NHIM), whose stable and unstable manifolds have sufficient dimensionality to act as separatrices, partitioning energy surfaces into regions of qualitatively distinct behavior. This NHIM forms the natural (dynamical) equator of a (spherical) dividing surface which locally divides an energy surface into two components (“reactants” and “products”), one on either side of the bottleneck. This dividing surface has all the desired properties sought for in transition state theory where reaction rates are computed from the flux through a dividing surface. In fact, the dividing surface that we construct is crossed exactly once by reactive trajectories, and not crossed by nonreactive trajectories, and related to these properties, minimizes the flux upon variation of the dividing surface.

We discuss three presentations of the energy surface and the phase space structures contained in it for 2-degree-of-freedom (DoF) systems in the three-dimensional space ?3, and two schematic models which capture many of the essential features of the dynamics for n-DoF systems. In addition, we elucidate the structure of the NHIM.} }

%

2009

@article {ArlinskiiHassiSnoo2009,

AUTHOR = {Arlinski{\u\i}, Yu.M. and Hassi, S. and de Snoo, H. S. V.}, TITLE = {Passive systems with a normal main operator and quasi-selfadjoint systems}, JOURNAL = {Complex Anal. Oper. Theory}, VOLUME = {3}, YEAR = {2009}, NUMBER = {1}, PAGES = {19--56}, URL = {http://dx.doi.org/10.1007/s11785-008-0060-3},

}

@article {BehrendtHassiSnoo2009,

AUTHOR = {Behrndt, J. and Hassi, S. and de Snoo, H.S.V.}, TITLE = {Boundary relations, unitary colligations, and functional models}, JOURNAL = {Complex Anal. Oper. Theory}, VOLUME = {3}, YEAR = {2009}, NUMBER = {1}, PAGES = {57--98}, URL = {http://dx.doi.org/10.1007/s11785-008-0064-z}

}

@article {BehrendtSnoo2009,

AUTHOR = {Behrndt, J. and de Snoo, H.S.V.}, TITLE = {On {K}re\u\i n's formula}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {351}, YEAR = {2009}, NUMBER = {2}, PAGES = {567--578}, URL = {http://dx.doi.org/10.1016/j.jmaa.2008.10.046},

}

@INCOLLECTION{Broer2009,

AUTHOR = {Broer, H.W.}, TITLE = {Normal Forms in Perturbation Theory}, EDITOR = {Robert A. Meyers}, BOOKTITLE = {Encyclopedia of Complexity and Systems Science}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2009}, URL = {http://www.springer.com/physics/complexity/book/978-0-387-75888-6}

}

@article {BroerCiocciHanssmannVanderbauwhede2009,

AUTHOR = {Broer, H.W. and Ciocci, M.C. and Han{\ss}mann, H. and Vanderbauwhede, A.}, TITLE = {Quasi-periodic stability of normally resonant tori}, JOURNAL = {Physica D}, VOLUME = {238}, YEAR = {2009}, PAGES = {309--318}, URL = {http://dx.doi.org/10.1016/j.physd.2008.10.004}, ABSTRACT = {We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.}

}

@INCOLLECTION{BroerHanssmann2009,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. }, TITLE = {Hamiltonian Perturbation Theory (and Transition to Chaos)}, EDITOR = {Robert A. Meyers}, BOOKTITLE = {Encyclopedia of Complexity and Systems Science}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2009}, URL = {http://www.springer.com/physics/complexity/book/978-0-387-75888-6}

}

@article {BroerHoltmanVegter2009,

AUTHOR = {Broer, H.W. and Holtman, S.J. and Vegter, G. and Vitolo, R.}, TITLE = {Geometry and dynamics of mildly degenerate Hopf-Neimarck-Sacker families near resonance}, JOURNAL = {Nonlinearity}, VOLUME = {22}, YEAR = {2009}, PAGES = {2161--2200}, URL = {http://dx.doi.org/10.1088/0951-7715/22/9/007}, ABSTRACT = {This paper deals with families of planar diffeomorphisms undergoing a Hopf–Ne?marck–Sacker bifurcation and focuses on bifurcation diagrams of the periodic dynamics. In our universal study the corresponding geometry is classified using Lyapunov–Schmidt reduction and contact-equivalence singularity theory, equivariant under an appropriate cyclic group. This approach recovers the non-degenerate standard Arnol'd resonance tongues. Our main concern is a mildly degenerate case, for which we analyse a 4-parameter universal model in detail. The corresponding resonance set has a Whitney stratification, which we explain by giving its incidence diagram and by giving both two- and three-dimensional cross-sections of parameter space. We investigate the further complexity of the dynamics of the universal model by performing a bifurcation study of an approximating family of Takens normal form vector fields. In particular, this study demonstrates how the bifurcation set extends an approximation of the resonance set of the universal model.}

}

@BOOK{BroerTakens2009,

AUTHOR = {Broer, H.W. and Takens, F.}, TITLE = {Dynamical Systems and Chaos}, PUBLISHER = {Epsilon Uitgaven}, YEAR = {2009},

}

@article {ChazottesColletRedigVerbitskiy2009,

AUTHOR = {Chazottes, J.-R. and Collet, P. and Redig, F. and Verbitskiy, E.}, TITLE = {A concentration inequality for interval maps with an indifferent fixed point}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {29}, YEAR = {2009}, NUMBER = {4}, PAGES = {1097--1117}, ISSN = {0143-3857}, MRCLASS = {37E05 (28Dxx 37Axx 37M10)}, MRNUMBER = {MR2529641}, DOI = {10.1017/S0143385708000588}, URL = {http://dx.doi.org/10.1017/S0143385708000588},

}

@article {DerkachHassiMalamudSnoo2009,

AUTHOR = {Derkach, V. A. and Hassi, S. and Malamud, M.M. and de Snoo, H.S.V.}, TITLE = {Boundary relations and generalized resolvents of symmetric operators}, JOURNAL = {Russ. J. Math. Phys.}, VOLUME = {16}, YEAR = {2009}, NUMBER = {1}, PAGES = {17--60}, URL = {http://dx.doi.org/10.1134/S1061920809010026}

}

@inproceedings{DettmannMorozovSieber2009,

AUTHOR = {Dettmann, C.P. and Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Systematization of All Resonance Modes in Circular Dielectric Cavities}, BOOKTITLE = {ICTON: 2009 11th International Conference on Transparent Optical Networks, Vols 1 and 2}, PAGES = {763--766}, YEAR = {2009}, URL = {http://dx.doi.org/10.1109/ICTON.2009.5185122}, ABSTRACT = {Circular dielectric cavities are key components for the construction of optic microresonators and microlasers. They are one of very few cases where the transcendental equations for complex eigenmodes (resonances) of an open system (dielectric cavity) can be found analytically in an exact manner. The behaviour of those eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analysed. The analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonance modes for both TM and TE polarizations. As a result, unambiguous azimuthal and radial modal indices are assigned to each internal and external resonance mode.}

}

@article {DettmannMorozovSieber2009b,

AUTHOR = {Dettmann, C.P. and Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Unidirectional emission from circular dielectric microresonators with a point scatterer}, JOURNAL = {Phys. Rev. A}, VOLUME = {80}, YEAR = {2009}, NUMBER = {6}, PAGES = {063813}, URL = {http://dx.doi.org/10.1103/PhysRevA.80.063813}, ABSTRACT = {Circular microresonators are micron-sized dielectric disks embedded in material of lower refractive index. They possess modes of extremely high Q-factors (low-lasing thresholds), which makes them ideal candidates for the realization of miniature laser sources. They have, however, the disadvantage of isotropic light emission caused by the rotational symmetry of the system. In order to obtain high directivity of the emission while retaining high Q-factors, we consider a microdisk with a pointlike scatterer placed off-center inside of the disk. We calculate the resulting resonant modes and show that some of them possess both of the desired characteristics. The emission is predominantly in the direction opposite to the scatterer. We show that classical ray optics is a useful guide to optimizing the design parameters of this system. We further find that exceptional points in the resonance spectrum influence how complex resonance wave numbers change if system parameters are varied.}

}

@article {DettmannMorozovSieber2009c,

AUTHOR = {Dettmann, C.P. and Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Internal and external resonances of dielectric disks}, JOURNAL = {Europhys. Lett.}, VOLUME = {87}, YEAR = {2009}, NUMBER = {3}, PAGES = {34003}, URL = {http://dx.doi.org/10.1209/0295-5075/87/34003}, ABSTRACT = {Circular microresonators (microdisks) are micron size dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analyzed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wave number plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well-defined azimuthal and radial modal indices.}

}

@article {DullinWaalkens2009,

AUTHOR = {Dullin, H.R. and Waalkens, H.}, TITLE = {Dullin and Waalkens reply [to comments by Eiglsperger et al. on the phase shift for 2D central scattering]}, JOURNAL = {Phys. Rev. Lett.}, VOLUME = {102}, YEAR = {2009}, NUMBER = {18}, PAGES = {188902}, URL = {http://dx.doi.org/10.1103/PhysRevLett.102.188902}, ABSTRACT = {Dullin and Waalkens reply to comments by Eiglsperger et al. (see ibid., vol. 102, 188901 (2009)). Dullin and Waalkens state that the results of their letter (see ibid., vol. 101, 070405 (2008)) are correct. In the letter they showed that the phase shift for 2D central scattering at a smooth repulsive potential cannot be uniquely defined as a globally smooth function of angular momentum and energy due to a topological obstruction similar to monodromy in bound systems.}

}

@article {EfstathiouLukinaSadovskii2009,

AUTHOR = {Efstathiou, K. and Lukina, O.V. and Sadovski{\'i}, D.A.}, TITLE = {Complete classification of qualitatively different perturbations of the hydrogen atom in weak near orthogonal electric and magnetic fields}, JOURNAL = {J. Phys. A}, VOLUME = {42}, YEAR = {2009}, NUMBER = {5}, PAGES = {055209}, URL = {http://dx.doi.org/10.1088/1751-8113/42/5/055209}, ABSTRACT = {We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near orthogonal configurations. Normalization of the Keplerian symmetry reveals that in the parameter space such systems belong in a `zone' of systems close to the 1:1 resonance, the latter corresponding to the exactly orthogonal configuration. Integrable approximations obtained from second normalization of systems in the 1:1 zone are classified into several different qualitative types, many of which possess nontrivial monodromy. We compute monodromy of the complete three-dimensional energy-momentum map, compare the joint quantum spectrum to classical bifurcation diagrams, and show the effect of second normalization to the joint spectrum.}

}

@article {EnterRuszel2009,

AUTHOR = {van Enter, A.C.D. and Ruszel, W.M.}, TITLE = {Gibbsianness versus non-Gibbsianness of time-evolved

planar rotor models},

JOURNAL = {Stoch. Proc. Appl.}, VOLUME = {431}, YEAR = {2009}, NUMBER = {119}, PAGES = {1866--1888}, URL = {doi:10.1016/j.spa.2008.09.005 }, ABSTRACT = {We study the Gibbsian character of time-evolved planar

rotor systems (that is, systems which have two-component, classical XY, spins) on View the MathML source, d≥2, in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure ?. We model the system with interacting Brownian diffusions View the MathML source moving on circles. We prove that for small times t and arbitrary initial Gibbs measures ?, or for long times and both high- or infinite-temperature initial measure and dynamics, the evolved measure ?t stays Gibbsian. Furthermore, we show that for a low-temperature initial measure ? evolving under infinite-temperature dynamics there is a time interval (t0,t1) such that ?t fails to be Gibbsian for d≥2. } }

@article {EzraWaalkensWiggins2009,

AUTHOR = {Ezra, G. S. and Waalkens, H. and Wiggins, S.}, TITLE = {Microcanonical rates, gap times, and phase space dividing surfaces}, JOURNAL = {J. Chem. Phys.}, VOLUME = {130}, YEAR = {2009}, NUMBER = {16}, PAGES = {164118}, URL = {http://dx.doi.org/10.1063/1.3119365}, ABSTRACT = {The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN reversible arrow CNH, previously studied using the methods of phase space transition state theory. Both algebraic (power law) and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale t less than or similar to 0.5 ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential (nonstatistical) decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.}

}

@article {FleurkeKuelske2009,

AUTHOR = {Fleurke, S. R. and K{\"u}lske, C.}, TITLE = {A Second-row Parking Paradox}, JOURNAL = {J. Stat. Phys.}, VOLUME = {136}, YEAR = {2009}, NUMBER = {2}, PAGES = {285--295}, URL = {http://dx.doi.org/10.1007/s10955-009-9775-4}, ABSTRACT = {We consider two variations of the discrete car parking problem where at every vertex of ? cars (particles) independently arrive with rate one. The cars can park in two lines according to the following parking (adsorption) rules. In both models a car which arrives at a given vertex tries to park in the first line first. It parks (sticks) whenever the vertex and all of its nearest neighbors are not occupied yet. A car that cannot park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded.

In the screening model a) a car cannot pass through parked cars in the second line with midpoints adjacent to its vertex of arrival. In the model without screening b) cars park according to the same rules, but parking in the first line cannot be obstructed by parked cars in the second line. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first- and second-line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.} }

@inproceedings{GaikoBroerHorsen2009,

AUTHOR = {Gaiko, V.A. and Broer, H.W. and van~Horsen, W.T.}, TITLE = {Limit cycles of a population dynamics model}, BOOKTITLE = {Proceedings of 4th International Scientific Conference on Physics and Control (PHYSCON 2009), September 2009, Catania, Italy}, YEAR = {2009}, PAGES = {1922--1925}, URL = {http://www.physcon2009.diees.unict.it/}

}

@article {GoussevSchubertWaalkensWiggins2009,

AUTHOR = {Goussev, A. and Schubert, R. and Waalkens, H. and Wiggins, S.}, TITLE = {The quantum normal form approach to reactive scattering: The cumulative reaction probability for collinear exchange reactions}, JOURNAL = {J. Chem. Phys.}, VOLUME = {131}, YEAR = {2009}, NUMBER = {14}, PAGES = {144103}, URL = {http://dx.doi.org/10.1063/1.3245402}, ABSTRACT = {The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy-atom systems such as the nitrogen-exchange reaction, the quantum normal form approach gives excellent results and has major computational benefits over full reactive scattering approaches. For light atom systems such as the hydrogen-exchange reaction however, the quantum normal approach is shown to give only poor results. This failure is attributed to the importance of tunneling trajectories in light atom reactions that are not captured by the quantum normal form as indicated by the only very slow convergence of the quantum normal form for such systems.}

}

@article {HalesWaalkens2009,

AUTHOR = {Hales, R. and Waalkens, H.}, TITLE = {Classical and quantum transport through entropic barriers modeled by hardwall hyperboloidal constrictions}, JOURNAL = {Ann. Phys.}, VOLUME = {324}, YEAR = {2009}, NUMBER = {7}, PAGES = {1408--1451}, URL = {http://dx.doi.org/10.1016/j.aop.2009.01.010}, ABSTRACT = {We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrodinger equation and the classical equations of motion for these geometries, we study in detail the quantum transmission probabilities and the associated quantum resonances, and relate them to the classical phase structures which govern the transport through the constrictions. These classical phase structures are compared to the analogous structures which, as has been shown only recently, govern reaction type dynamics in smooth systems. Although the systems studied in this paper are special due their separability they can be taken as a guide to study entropic barriers resulting from constriction geometries that lead to non-separable dynamics.}

}

@article {HassiSebestyenSnoo2009,

AUTHOR = {Hassi, S. and Sebesty{\'e}n, Z. and de Snoo, H.S.V.}, TITLE = {Lebesgue type decompositions for nonnegative forms}, JOURNAL = {J. Funct. Anal.}, VOLUME = {257}, YEAR = {2009}, NUMBER = {12}, PAGES = {3858--3894}, URL = {http://dx.doi.org/10.1016/j.jfa.2009.09.014}

}

@article{HassiSebestyenSnoo2009b,

AUTHOR = {Hassi, S. and Sebesty{\'e}n, Z. and de~Snoo, H.S.V.}, TITLE = {Domain and range descriptions for adjoint relations,

and parallel sums and differences of forms},

JOURNAL = {Oper. Theory Adv. Appl.}, VOLUME = {198}, YEAR = {2009}, PAGES = {211--227},

}

@article {HassiSnooSzafraniec2009,

AUTHOR = {Hassi, S. and de~Snoo, H.S.V. and Szafraniec, F.H.}, TITLE = {Componentwise and canonical decompositions of linear relations}, JOURNAL = {Dissertationes Math.}, VOLUME = {465}, YEAR = {2009}, PAGES = {1--59}, URL={http://journals.impan.gov.pl/dm/Inf/465-0-1.html}, ABSTRACT = {Let A be a, not necessarily closed, linear relation in a Hilbert space H with a multivalued part mulA. An operator B in H with ranB ? mulA?? is said to be an operator part of A when A = B +b ({0} ? mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for an operator part are established via the so-called canonical decomposition of A. In addition, conditions are developed for the above decomposition to be orthogonal (components defined in orthogonal subspaces of the underlying space). Such orthogonal decompositions are shown to be valid for several classes of relations. The relation A is said to have a Cartesian decomposition if A = U + i V , where U and V are symmetric relations and the sum is operatorwise. The connection between a Cartesian decomposition of A and the real and imaginary parts of A is investigated.}

}

@article {HoekstraVogelzangVerbitskiyNijsten2009,

AUTHOR = {Hoekstra, M. and Vogelzang, M. and Verbitskiy, E. and Nijsten, M.}, TITLE = {Health technology assessment review: Computerized glucose regulation in the intensive care unit - how to create artificial control}, JOURNAL = {Critical Care}, VOLUME = {13:223}, YEAR = {2009}, }

@PHDTHESIS{Holtman2009,

AUTHOR = {Holtman, Sijbo J.}, TITLE = {Dynamics and geometry near resonant bifurcations}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {September}, YEAR = {2009}, NOTE = {Advisors: H.W. Broer and G. Vegter, 136 pages}, URL = {http://irs.ub.rug.nl/ppn/321620194}

}

@PHDTHESIS{Opoku2009,

AUTHOR = {Opoku, Alex A.}, TITLE = {On Gibbs properties of transforms of lattice and

mean-field systems},

SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer

Science},

MONTH = {September}, YEAR = {2009}, NOTE = {Advisors: C. K\"ulske, A.C.D. van Enter and H.W.

Broer, 139 pages},

URL = {http://irs.ub.rug.nl/ppn/321247396}

}

@article {SandoviciSnoo2009,

AUTHOR = {Sandovici, A. and de Snoo, H.S.V.}, TITLE = {An index formula for the product of linear relations}, JOURNAL = {Linear Algebra Appl.}, VOLUME = {431}, YEAR = {2009}, NUMBER = {11}, PAGES = {2160--2171}, URL = {http://dx.doi.org/10.1016/j.laa.2009.07.011}

}

@article{SHBAGVCB2009,

AUTHOR={Sazonov, A.V. and Ho, C. K. and Bergmans, J. W. M. and Arends, J. B. A. M. and Griep, P. A. M. and Verbitskiy, E.A. and Cluitmans, P. J. M. and Boon, P.A. J. M. }, TITLE={An investigation of the phase locking index for measuring of interdependency of cortical source signals recorded in the EEG}, JOURNAL={Biological Cybernetics}, YEAR={2009}, VOLUME={100}, NUMBER={2}, PAGES={129--146},

}

@article {SchmidtVerbitskiy2009,

AUTHOR = {Schmidt, Klaus and Verbitskiy, Evgeny}, TITLE = {Abelian sandpiles and the harmonic model}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {292}, YEAR = {2009}, NUMBER = {3}, PAGES = {721--759}, ISSN = {0010-3616}, CODEN = {CMPHAY}, MRCLASS = {37Bxx (82Bxx)}, MRNUMBER = {MR2551792}, DOI = {10.1007/s00220-009-0884-3}, URL = {http://dx.doi.org/10.1007/s00220-009-0884-3},

}

@article {SchubertWaalkensWiggins2009,

AUTHOR = {Schubert, R. and Waalkens, H. and Wiggins, S.}, TITLE = {A Quantum Version of {W}igner's Transition State Theory}, JOURNAL = {Few-Body Systems}, VOLUME = {45}, YEAR = {2009}, NUMBER = {2-4}, PAGES = {203--206}, URL = {http://dx.doi.org/10.1007/s00601-009-0037-4}, ABSTRACT = {A quantum version of a recent realization of Wigner's transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in (h) over bar. This leads to an explicit algorithm to compute cumulative quantum reaction rates and the associated Gamov-Siegert resonances with high accuracy. This algorithm is very efficient since, as opposed to other approaches, it requires no quantum time propagation.}

}

@article {Waalkens2009,

AUTHOR = {Waalkens, H.}, TITLE = {Quantum transition state theory}, JOURNAL = {Bulletin Am. Phys. Soc.}, VOLUME = {51}, YEAR = {2009}, ABSTRACT = {The main idea of Wigner's transition state theory (TST) is to compute reaction rates from the flux through a dividing surface placed between reactants and products. In order not to overestimate the rate the dividing surface needs to have the no- recrossing property, i.e. reactive trajectories cross the dividing surface exactly once, and nonreactive trajectories do not cross it at all. The long standing problem of how to construct such a diving surface for multi-degree-of-freedom systems was solved only recently using ideas from dynamical systems theory. Here a normal form allows for a local decoupling of the classical dynamics which leads to the explicit construction of the phase space structures that govern the reaction dynamics through transition states. The dividing surface is spanned by a normally hyperbolic manifold which is the mathematical manifestation of the transition state as an unstable invariant subsystem of one degree of freedom less than the full system. The mere existence of a quantum version of TST is discussed controversially in the literature. The key isssue is the presence of quantum mechanical tunneling which prohibits the existence of a local theory analogous to the classical case. Various approaches have been devloped to overcome this problem by propagating quantum wavefunctions through the transition state region. These approaches have in common that they are computationally very expensive which seriously limits their applicability. In contrast the approach by Roman Schubert, Stephen Wiggins and myself is local in nature. A quantum normal form allows us to locally decouple the quantum dynamics to any desired order in Planck's constant. This yields not only the location of the scattering and resonance wavefunctions relative to the classical phase space structures, but also leads to very efficient algorithms to compute cumulative reaction probabilities and Gamov-Siegert resonances which are the quantum imprints of the transition state.}

}

%

2008

@article {BehrndtHassiSnoo2008,

AUTHOR = {Behrndt, J. and Hassi, S. and de~Snoo, H.S.V.}, TITLE = {Functional models for Nevanlinna families}, JOURNAL = {Opuscula Mathematica}, VOLUME = {28}, YEAR = {2008}, PAGES = {233--245}

}

@article {BroerEfstathiouSubramanian2008,

AUTHOR = {Broer, H.W. and Efstathiou, K. and Subramanian, E.}, TITLE = {Robustness of unstable attractors in arbitrarily sized pulse-coupled systems with delay}, JOURNAL = {Nonlinearity}, VOLUME = {21}, YEAR = {2008}, PAGES = {13--49}

}

@article {BroerEfstathiouSubramanian2008b,

AUTHOR = {Broer, H.W. and Efstathiou, K. and Subramanian, E.}, TITLE = {Heteroclinic cycles between unstable attractors}, JOURNAL = {Nonlinearity}, VOLUME = {21}, YEAR = {2008}, PAGES = {1385--1410}

}

@article {BroerHoltmanVegter2008,

AUTHOR = {Broer, H.W. and Holtman, S.J. and Vegter, G.}, TITLE = {Recognition of the bifurcation type of resonance in mildly degenerate {H}opf-{N}eimark-{S}acker families}, JOURNAL = {Nonlinearity}, VOLUME = {21}, YEAR = {2008}, PAGES = {2463--2482}

}

@article {BroerSimoVitolo2008,

AUTHOR = {Broer, H.W. and Sim{\'o}, C. and Vitolo, R.}, TITLE = {The {H}opf-{S}addle-{N}ode bifurcation for fixed points of 3{D}-diffeomorphisms, analysis of a resonance `bubble'}, JOURNAL = {Physica D}, VOLUME = {237}, YEAR = {2008}, PAGES = {1773--1799}

}

@article {BroerSimoVitolo2008b,

AUTHOR = {Broer, H.W. and Sim{\'o}, C. and Vitolo, R.}, TITLE = {The {H}opf-{S}addle-{N}ode bifurcation for fixed points of 3{D}-diffeomorphisms, the {A}rnol'd resonance web}, JOURNAL = {Bull. Belgian Math. Soc. Simon Stevin}, VOLUME = {15}, YEAR = {2008}, PAGES = {769--787}

}

@article {BroerVegter2008,

AUTHOR = {Broer, H.W. and Vegter, G.}, TITLE = {Generic {H}opf-{N}e\u{\i}mark-{S}acker bifurcations in feed forward systems}, JOURNAL = {Nonlinearity}, VOLUME = {21}, YEAR = {2008}, PAGES = {1547--1578}

}

@article {BroerVitolo2008,

AUTHOR = {Broer, H.W. and Vitolo, R.}, TITLE = {Dynamical systems modeling of low-frequency variability in low-order atmospheric models}, JOURNAL = {Discrete and Continous Dynamical Systems - Series B}, VOLUME = {10}, NUMBER = {2/3} YEAR = {2008}, PAGES = {401--419}

}

@article {DehlingFleurkeKulske2008,

AUTHOR = {Dehling, B.H. Fleurke, S. and K{\"u}lske, C.}, TITLE = {Parking on a random tree}, JOURNAL = {J. Stat. Phys.}, VOLUME = {133}, NUMBER = {1} YEAR = {2008}, PAGES = {151--157}

}

@article {DettmannMorozovSieberWaalkens2008,

AUTHOR = {Dettmann, C.P. and Morozov, G.V. and Sieber, M. and Waalkens, H.}, TITLE = {Directional Emission from an Optical Microdisk Resonator with a Point Scatterer}, JOURNAL = {Europhys. Lett.}, VOLUME = {82}, YEAR = {2008}, PAGES = {34002}

}

@article {DullinWaalkens2008,

AUTHOR = {Dullin, H.R. and Waalkens, H.}, TITLE = {Nonuniqueness of the Phase Shift in Central Scattering due to Monodromy}, JOURNAL = {Phys. Rev. Lett.}, VOLUME = {101}, YEAR = {2008}, PAGES = {070405}

}

@article {EfstathiouLukinaSadovskii2008,

AUTHOR = {Efstathiou, K. and Lukina, O.V. and Sadovski{\'i}, D.A.}, TITLE = {Most typical 1:2 resonant perturbation of the hydrogen atom by weak electric and magnetic fields}, JOURNAL = {Phys. Rev. Lett.}, VOLUME = {101}, YEAR = {2008}, PAGES = {253003}

}

@article {EnterKulske2008,

AUTHOR = {van~Enter, A.C.D. and C. K\"ulske, C.}, TITLE = {Non-existence of random gradient Gibbs measures in continuous interface models in d=2}, JOURNAL = {Ann. Appl. Prob.}, VOLUME = {18}, NUMBER = {1}, YEAR = {2008}, PAGES = {109--119}

}

@article {EnterRuszel2008,

AUTHOR = {van~Enter, A.C.D. and Ruszel, W.M.}, TITLE = {Loss and recovery of Gibbsianness for XY models in small external fields}, JOURNAL = {J. Math. Phys.}, VOLUME = {49}, NUMBER = {12}, YEAR = {2008}, PAGES = {125208}

}

@article {EnterRedigVerbitskiy2008,

AUTHOR = {van~Enter, A.C.D. and Redig, F. and Verbitskiy, E.}, TITLE = {Gibbsian and non-Gibbsian states at Eurandom}, JOURNAL = {Stat. Neerlandica}, VOLUME = {62}, NUMBER = {3}, YEAR = {2008}, PAGES = {331--344}

}

@article {HassiSandoviciSnooWinkler2008,

AUTHOR = {Hassi, S. and Sandovici, A. and de~Snoo, H.S.V. and Winkler, H.}, TITLE = {One-dimensional perturbations, asymptotic expansions, and spectral gaps}, JOURNAL = {Oper. Theory Adv. Appl.}, VOLUME = {188}, YEAR = {2008}, PAGES = {149--173}

}

@article {KulskeOpoku2008,

AUTHOR = {K{\"u}lske, C. and Opoku, A.}, TITLE = {The posterior metric and the goodness of Gibbsianness for transforms of Gibbs measures}, JOURNAL = {El. J. Prob.}, VOLUME = {13}, YEAR = {2008}, PAGES = {1307--1344}

}

@article {KulskeOpoku2008b,

AUTHOR = {K{\"u}lske, C. and Opoku, A.}, TITLE = {Continuous-spin mean-field models: limiting kernels and Gibbs properties of local transforms}, JOURNAL = {J. Math. Phys.}, VOLUME = {49}, NUMBER = {12}, YEAR = {2008}, PAGES = {125215}

}

@article {KulskeOrlandi2008,

AUTHOR = {K{\"u}lske, C. and Orlandi, E.}, TITLE = {Continuous interfaces with disorder: Even strong pinning is too weak in 2 dimensions}, JOURNAL = {Stoch. Proc. Appl.}, VOLUME = {118}, NUMBER = {11}, YEAR = {2008}, PAGES = {1973--1981}

}

@article {LaCourJansenRuszel2008,

AUTHOR = {LaCour Jansen, T. and Ruszel, W.M.}, TITLE = {Narrowing in the time-averaging approximation for simulating two-dimensional nonlinear infrared spectra}, JOURNAL = {J. Chem. Phys.}, VOLUME = {128}, YEAR = {2008}, PAGES = {214501}

}

@PHDTHESIS{Lukina2008,

AUTHOR = {Lukina, Olga V.}, TITLE = {Geometry of torus bundles in integrable Hamiltonian systems}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Johann Bernoulli Institute for Mathematics and Computer Science}, MONTH = {September}, YEAR = {2008}, NOTE = {Advisor: H.W. Broer, 105 pages}, URL = {http://irs.ub.rug.nl/ppn/314417303}

}

@article {LukinaTakensBroer2008,

AUTHOR = {Lukina, O.V. and Takens, F. and Broer, H.W.}, TITLE = {Global properties of integrable Hamiltonian systems}, JOURNAL = {Regular and Chaotic Dynamics}, VOLUME = {13}, NUMBER = {6}, YEAR = {2008}, PAGES = {588--630}

}

@article {WaalkensSchubertWiggins2008,

AUTHOR = {Waalkens, H. and Schubert, R. and Wiggins, S.}, TITLE = {Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum}, JOURNAL = {Nonlinearity}, VOLUME = {21}, YEAR = {2008}, PAGES = {R1--R118}

}

%

2007

@article { ArlinskiuiHassiSnoo2007,

AUTHOR = { Arlinski{\i}, Yu.M. and Hassi, S and de~Snoo, H.S.V. }, TITLE = { Parametrization of contractive block operator matrices and passive discrete systems }, JOURNAL = { Complex Analysis Operator Theory }, VOLUME = {1}, YEAR = {2007}, % NUMBER = {}, PAGES = {211--233}, }

@article { Behrndt2007,

AUTHOR = { Behrndt, J.}, TITLE = { On the spectral theory of singular indefinite Sturm-Liouville operators }, JOURNAL = { J. Math. Anal. Appl. }, VOLUME = {334}, YEAR = {2007}, % NUMBER = {}, PAGES = {1439--1449}, }

@article { BehrndtLanger2007,

AUTHOR = { Behrndt, J. and Langer, M.}, TITLE = { Boundary value problems for elliptic partial differential

operators on bounded domains },

JOURNAL = { J. Funct. Anal. }, VOLUME = {243}, YEAR = {2007}, % NUMBER = {}, PAGES = {536--565}, }

@article { BehrndtLuger2007,

AUTHOR = { Behrndt, J. and Luger, A.}, TITLE = { An analytic characterization of the eigenvalues of self-adjoint

extensions },

JOURNAL = { J. Funct. Anal. }, VOLUME = {242}, YEAR = {2007}, % NUMBER = {}, PAGES = {607--640}, }

@article { BehrndtLugerTrunk2007,

AUTHOR = { Behrndt, J. and Luger, A. and Trunk, C.}, TITLE = { Generalized resolvents of a class of symmetric

operators in Krein spaces },

JOURNAL = { Oper. Theory. Adv. Appl. }, VOLUME = {175}, YEAR = {2007}, % NUMBER = {}, PAGES = {13--32},

}

@article { BehrndtTrunk2007,

AUTHOR = { Behrndt, J. and Trunk, C.}, TITLE = { On the negative squares of indefinite Sturm-Liouville operators, }, JOURNAL = { J. Diff. Eqns. }, VOLUME = {238}, YEAR = {2007}, % NUMBER = {}, PAGES = {491--519}, }

@article { BelyiHassiSnooTsekanovskii2007,

AUTHOR = {Belyi, S. and Hassi, S. and de Snoo, H.S.V. and Tsekanovski{\i}, E.R.}, TITLE = {A general realization problem for matrix-valued Herglotz-Nevanlinna functions}, JOURNAL = { Lin Alg. Appl. }, VOLUME = {419}, YEAR = {2007}, % NUMBER = {}, PAGES = {331--358},

}

@article {Broer2007,

AUTHOR = {Broer, H.W.}, TITLE = {Computergebruik en demathematisering }, JOURNAL = {Nieuw Arch. Wisk. 5th series}, VOLUME = {5}, YEAR = {2007}, NUMBER = {3}, PAGES = {201--206},

}

@article {BroerCiocciHanssmann2007,

AUTHOR = {Broer, H.W. and Ciocci, M.C. and Han{\ss}mann, H.}, TITLE = {The quasi-periodic reversible Hopf bifurcation}, JOURNAL = {IJBC}, VOLUME = {17}, YEAR = {2007}, NUMBER = {8}, PAGES = {2605--2623},

}

@article { BroerCushmanFassoTakens2007,

AUTHOR = {Broer, H.W. and Cushman, R.H. and Fass{\'o}, F. and Takens, F.}, TITLE = {Geometry of {\sc kam} tori for nearly integrable Hamiltonian systems}, JOURNAL = {Ergod. Th. \&Dynam. Sys. }, VOLUME = {27}, YEAR = {2007}, % NUMBER = {}, PAGES = {725--741}, }

@inproceedings{BroerDijkVitolo2007,

```
AUTHOR = {Broer, H.W. and Van Dijk, R. and Vitolo, R.},
TITLE = { Survey of strong normal-interenal $k:\ell$ resonances in
```

quasi-periodically driven oscillators for $\ell = 1,2,3.$},

BOOKTITLE = { Symmetry and Perturbation Theory,

Proc. Int. Conf. SPT },

PAGES = {45--55}, YEAR = {2007}

}

@inproceedings{BroerGolubitskyVegter2007,

AUTHOR = {Broer, H.W. and Golubitsky, M. and Vegter, G.}, TITLE = {Geometry of resonance tongues}, BOOKTITLE = { Singularity Theory, Proc. 2005 Marseille Singularity School and Conference,

dedicated to Jean-Paul Brasselet on His 60th Birthday },

PAGES = {327--356}, YEAR = {2007}, }

@article { BroerHagenVegter2007,

AUTHOR = {Broer, H.W. and Hagen, A. and Vegter, G.}, TITLE = {Numerical continuation of normally hyperbolic invariant manifolds}, JOURNAL = {Nonlinearity }, VOLUME = {20}, YEAR = {2007}, % NUMBER = {}, PAGES = {1499--1534},

}

@article { BroerHanssmannHoo2007,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. and Hoo, J.}, TITLE = {The quasi-periodic Hamiltonian Hopf bifurcations}, JOURNAL = {Nonlinearity }, VOLUME = {20}, YEAR = {2007}, % NUMBER = {}, PAGES = {417--460},

}

@article { BroerHooNaudot2007,

AUTHOR = {Broer, H.W. and Hoo, J. and Naudot, V.}, TITLE = {Normal linear stability of quasi-periodic tori}, JOURNAL = {J. Diff. Eqns. }, VOLUME = {232}, YEAR = {2007}, NUMBER = {2}, PAGES = {355--418},

}

@article { BroerNaudotRoussarieSaleh2007,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R. and Saleh, K.}, TITLE = {Dynamics of a predator-prey model with non-monotonic response function}, JOURNAL = {DCDS}, VOLUME = {18}, YEAR = {2007}, NUMBER = {2\&3}, PAGES = {221--251},

}

@article {BroerNaudotRoussarieSalehWagener2007,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R. and Saleh, K. and Wagener, F.O.O.}, TITLE = {Organising centres in the semi-global analysis of dynamical systems}, JOURNAL = {IJAMAS}, VOLUME = {12}, YEAR = {2007}, NUMBER = {D07}, PAGES = {7--36}

}

@article { BroerTakens2007,

AUTHOR = {Broer, H.W. and Takens, F.}, TITLE = {Unicity of {\sc kam} tori}, JOURNAL = {Ergod. Th. \&Dynam. Sys. }, VOLUME = {27}, YEAR = {2007}, % NUMBER = {}, PAGES = {713--724},

}

@article {ChazottesColletKulskeRedig2007,

AUTHOR = {Chazottes, J.-R. and Collet, P. and K{\"u}lske, C. and Redig, F.}, TITLE = {Concentration inequalities for random fields via coupling}, JOURNAL = {Probab. Theory Related Fields}, VOLUME = {137}, YEAR = {2007}, NUMBER = {1{\&}2}, PAGES = {201--225}

}

@inproceedings{DerkachHassiSnoo2007,

AUTHOR = {Derkach, V.A. and Hassi, S. and De Snoo, H.S.V. }, TITLE = {Asymptotic expansions of generalized Nevanlinna functions and their spectral properties}, BOOKTITLE = {Oper. Theory Adv. Appl., vol. 175}, PAGES = {51--88}, YEAR = {2007}, }

@article {EfstathiouSadovskiiCushman2007,

```
AUTHOR = {Efstathiou, K. and Sadovski{\'\i}, D.A. and Cushman, R.H. },
TITLE = {Fractional monodromy in the $1{:}-2$ resonance},
JOURNAL = {Adv. In Math.},
VOLUME = {209},
YEAR = {2007},
% NUMBER = {},
PAGES = {241--273},
}
```

@article {EfstathiouSadovskiiZhilinskii2007,

AUTHOR = {Efstathiou, K. and Sadovski{\'\i}, D.A. and, Zhilinski{\’\i}, B.I. }, TITLE = {Classification of perturbations of the hydrogen atom by small static electric and magnetic fields}, JOURNAL = {Proc. Roy. Soc. London Ser. A.}, VOLUME = {463}, YEAR = {2007}, % NUMBER = {}, PAGES = {1771--1790},

}

@article {Enter2007,

AUTHOR = {Van Enter, A.C.D.}, TITLE = {Alleen maar verliezers? De volgende aflevering in de affaire-Debije}, JOURNAL = {Nederlands Tijdschrift voor Natuurkunde}, VOLUME = {73}, YEAR = {2007}, NUMBER = {6}, PAGES = {170}, }

@article {EnterHulshof2007,

AUTHOR = {Van Enter, A.C.D. and Hulshof, W.J.T.}, TITLE = {Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections}, JOURNAL = {J. Stat. Phys.}, VOLUME = {128}, YEAR = {2007}, NUMBER = {6}, PAGES = {1383--1389}, }

@article {EnterKulske2007,

AUTHOR = {Van Enter, A.C.D. and K{\"u}lske, C.}, TITLE = {Two connections between random systems and non-Gibbsian measures}, JOURNAL = {J. Stat. Phys.}, VOLUME = {126}, YEAR = {2007}, NUMBER = {4\&5}, PAGES = {1007--1024},

}

@article {EnterRuszel2007,

AUTHOR = {Van Enter, A.C.D. and Ruszel, W.M.}, TITLE = {Chaotic temperature dependence at zero temperature}, JOURNAL = {J. Stat. Phys.}, VOLUME = {127}, YEAR = {2007}, NUMBER = {3}, PAGES = {567--573},

}

@article {EnterShlosman2007,

AUTHOR = {Van Enter, A.C.D. and Shlosman, S.B.}, TITLE = {First-order transitions for very nonlinear sigma models}, JOURNAL = {Mark. Proc. Rel. Fields}, VOLUME = {13}, YEAR = {2007}, NUMBER = {2}, PAGES = {239--249},

}

@article {HassiSandoviciSnooWinkler2007,

AUTHOR = {Hassi, S. and Sandovici, A. and De Snoo, H.S.V. and Winkler, H.}, TITLE = {A general factorization approach to the extension theory of nonnegative operators and relations}, JOURNAL = {J. Operator Theory}, VOLUME = {58}, YEAR = {2007}, %NUMBER = {}, PAGES = {351--386},

}

@article {HassiSandoviciSnooWinkler2007b,

AUTHOR = {Hassi, S. and Sandovici, A. and De Snoo, H.S.V. and Winkler, H.}, TITLE = {Extremal extensions for the sum of nonnegative selfadjoint relations}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {135}, YEAR = {2007}, %NUMBER = {}, PAGES = {3193--3204},

}

@article {HassiSebestyenSnooSzafraniec2007,

AUTHOR = {Hassi, S. and Sebesty{\'}en, Z. and De Snoo, H.S.V. and Szafraniec, F.H.}, TITLE = {A canonical decomposition for linear operators and linear relations}, JOURNAL = {Acta Math. Hungar.}, VOLUME = {115}, YEAR = {2007}, %NUMBER = {}, PAGES = {281--307}, }

@inbook{HassiSnooSterkWinkler2007, author = {Hassi, S. and de Snoo, H.S.V. and Sterk, A.E. and Winkler, H.}, title = {Finite-dimensional graph perturbations of selfadjoint Sturm-Liouville problems}, pages = {205--228}, volume = {Operator Theory, Structured Matrices, and Dilations: Tiberiu Constantinescu Memorial Volume}, publisher= {The Theta Foundation}, editor = {Bakonyi, M. and Gheondea, A. and Putinar, M. and Rovnjak, J.}, year = {2007} }

@inproceedings{HassiSnooWinkler2007b,

AUTHOR = {Hassi, S. and De Snoo, H.S.V. and Winkler, H.}, TITLE = {On exceptional extensions close to the generalized Friedrichs extension of symmetric operators}, BOOKTITLE = {Oper. Theory Adv. Appl., vol. 175}, PAGES = {111--120}, YEAR = {2007}, }

@article {KulskeLeNy2007,

AUTHOR = {K{\"u}lske, C. and Le Ny, A.}, TITLE = {Spin-flip dynamics of the Curie-Weiss model: Loss of Gibbsianness with possibly broken symmetry}, JOURNAL = {Comm. Math. Phys.}, VOLUME = {271}, YEAR = {2007}, NUMBER = {2}, PAGES = {431--454}, }

@article {SandoviciSnooWinkler2007,

AUTHOR = {Sandovici, A. and De Snoo, H.S.V. and Winkler, H.}, TITLE = {Ascent, descent, nullity, and defect for linear relations in linear spaces}, JOURNAL = {Lin. Alg. Appl.}, VOLUME = {423}, YEAR = {2007}, %NUMBER = {}, PAGES = {456--497}, }

@inproceedings{SazonovHoBergmansArendsGriepVerbitskiyCluitmansBoon2007,

AUTHOR = {Sazonov, A.V. and Ho, C.K. and Bergmans, J.W.M. and Arends, J.B.A.M. and Griep, P.A.M. and Verbitskiy, E.A. and Cluitmans, P.J.M. and Boon, P.A.J.M.}, TITLE = {Analysis of the Phase Locking Index for Measuring of Interdependency of Cortical Signals Recorded in the EEG}, BOOKTITLE = {Engineering in Medicine and Biology Society, Proc. 29th Annual Int. Conf. IEEE}, PAGES = {1985--1991}, YEAR = {2007}, }

@inproceedings{SazonovHoBergmansArendsGriepVerbitskiyCluitmansBoon2007b,

AUTHOR = {Sazonov, A.V. and Ho, C.K. and Bergmans, J.W.M. and Arends, J.B.A.M. and Griep, P.A.M. and Verbitskiy, E.A. and Cluitmans, P.J.M. and Boon, P.A.J.M.}, TITLE = {Analysis of the Phase Locking Index for Measuring of Interdependency of Cortical Signals Recorded in the EEG}, BOOKTITLE = {Engineering in Medicine and Biology Society, Proc. 29th Annual Int. Conf. IEEE}, PAGES = {1985--1991}, YEAR = {2007}, }

@inproceedings{SchoenmakersTjoelkerTuylsVerbitskiy2007,

AUTHOR = {Schoenmakers, L.A.M. and Tjoelker, J. and Tuyls, P.T. and Verbitskiy, E.A..}, TITLE = {Smooth R\’enyi entropy of ergodic quantum informations sources}, BOOKTITLE = {Proc. 2007 IEEE Int. Symposium on Information Theory (ISIT)}, % PAGES = {}, YEAR = {2007}, }

@PHDTHESIS{Sitters2007

AUTHOR = {Sitters, H.}, TITLE = { Sybrandt Hansz Cardinael 1578-1647, Rekenmeester en wiskundige, zijn leven en zijn werk }, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Research Institute of Mathematics and Computing Science}, MONTH = {November} YEAR = {2007}, NOTE = {Advisors: H.W. Broer and J.A. van Maanen (UU), 664 pages},

}

@inproceedings{VitoloBroerSimo2007,

AUTHOR = {Vitolo, R. and Broer, H.W. and Sim{\'o}, C.}, TITLE = {The Hopf-saddle-node for fixed points of 3d-diffeomorphisms}, BOOKTITLE = {Symmetry and Perturbation Theory, Proc. Int. Conf. SPT}, PAGES = {280-281}, YEAR = {2007}, }

%

2006

@inbook{ArlinskiiHassiSnoo2006, author = {Arlinski{\u{i}}, Yu. M. and Hassi, S. and de Snoo, H.S.V.}, title = {$Q$-functions of quasi-selfadjoint contractions }, pages = {23--54}, volume = {163}, publisher= {Oper. Theory Adv. Appl.}, %editor = {}, year = {2006} }

@article {BehrndtJonas2006,

AUTHOR = {Behrndt, J and Jonas, P.}, TITLE = {Boundary value problems with local generalized Nevanlinna functions in the boundary condition}, JOURNAL = {Integral Equations Operator Theory}, VOLUME = {56}, YEAR = {2006}, %NUMBER = {}, PAGES = {453--475}, }

@article {BehrndtPhilippTrunk2006,

AUTHOR = {Behrndt, J and Philipp, F. and Trunk, C.}, TITLE = {Properties of the spectrum of type $\pi_+$ and type $\pi_-$ of self-adjoint

operators in Krein spaces},

JOURNAL = {Methods Funct. Anal. Topoloty}, VOLUME = {12}, YEAR = {2006}, %NUMBER = {}, PAGES = {326--340}, }

@article {BehrndtTrunk2006,

AUTHOR = {Behrndt, J and Trunk, C.}, TITLE = {Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions}, JOURNAL = {J. Diff. Eqns.}, VOLUME = {222}, YEAR = {2006}, %NUMBER = {}, PAGES = {297--324}, }

@inproceedings{Behrndt2006,

AUTHOR = {Behrndt, J.}, TITLE = {Linearizations of a class of elliptic boundary value problems}, BOOKTITLE = {Proc. Appl. Math. Mech., Vol 6}, PAGES = {619--620}, YEAR = {2006}, }

@inproceedings{BehrndtMalamudNeidhardt2006,

AUTHOR = {Behrndt, J. and Malamud, M.M. and Neidhardt, H.}, TITLE = {Scattering systems and characteristic functions}, BOOKTITLE = {Proc. 17th Int. Symposium on Mathematical Theory of Networks and Systems (MTNS)}, PAGES = {1940--1945}, YEAR = {2006}, }

@inproceedings{BroerHanssmannHooNaudot2006,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. and Hoo, J. and Naudot, V.}, TITLE = {Nearly-integrable perturbations of the Lagrange top: applications

of {\sc kam} theory },

BOOKTITLE = {Dynamics and Stochastics Festschrift in Honor of M.S. Keane, Lecture Notes – Monograph Series, Vol 48}, PAGES = {286--303}, YEAR = {2006}, }

@inproceedings{BroerHagenVegter2006,

AUTHOR = {Broer, H.W. and Hagen, A. and Vegter, G.}, TITLE = {A versatile algorithm for computing invariant manifolds}, BOOKTITLE = {Model Reduction and Coars-Graining Approaching for Multiscale Phenomena} PAGES = {17--38}, YEAR = {2006}, }

@article {BroerHanssmannYou2006,

AUTHOR = {Broer, H.W. and Hans{\ss}mann, H. and You, J.}, TITLE = {Umbilical torus bifurcations in Hamiltonian systems}, JOURNAL = {J. Diff. Eqns.}, VOLUME = {222}, YEAR = {2006}, %NUMBER = {}, PAGES = {233--262}, }

@article {BroerNaudotRoussarieSaleh2006,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R. and Saleh, K.}, TITLE = {A predator-prey model with non-monotonic response function}, JOURNAL = {Regular and Chaotic Dynamics}, VOLUME = {11}, YEAR = {2006}, NUMBER = {2}, PAGES = {155--165}, }

@article {BroerNaudotRoussarie2006,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R. }, TITLE = {Catastrophe theory in Dulac unfoldings}, JOURNAL = {Ergod. Th. \&Dynam. Sys.}, VOLUME = {26}, YEAR = {2006}, %NUMBER = {}, PAGES = {1--35}, }

@article {Broer2006,

AUTHOR = {Broer, H.W.}, TITLE = {Wiskunde als kritische succesfactor?}, JOURNAL = {Euclides}, VOLUME = {81}, YEAR = {2006}, NUMBER = {6}, PAGES = {282--285}, }

@article {ChazottesColletKulskeRedig2006,

AUTHOR = {Chazottes, J.R. and Collet, P. and K{\"u}lske, C. and Redig, F. }, TITLE = {Deviation inequalities via coupling for stochastic processes and random fields}, JOURNAL = {published online in Prob. Theory Related Fields, DOI 10.1007/s00440-006-0026-1}, VOLUME = {}, YEAR = {2006}, %NUMBER = {}, PAGES = {22}, }

@inbook{DerkachHassiSnoo2006, author = {Derkach, V.A. and Hassi, S. and de Snoo, H.S.V.}, title = {A factorization model for the generalized Friedrichs extensions in a Pontryagin space}, pages = {117--133}, volume = {162}, publisher= {Oper. Theory Adv. Appl.}, %editor = {}, year = {2006} }

@article {DerkachHassiMalamudSnoo2006,

AUTHOR = {Derkach, V.A. and Hassi, S. and Malamud, M.M. and de Snoo, H.S.V. }, TITLE = {Boundary relations and their Weyl families}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {358}, YEAR = {2006}, %NUMBER = {}, PAGES = {5351--5400}, }

@article {EnterKulske2006,

AUTHOR = {van Enter, A.C.D. and K{\"u}lske, C. }, TITLE = {Two connections between random systems and non-Gibbsian measures}, JOURNAL = { published Online in J.Statist.Phys: DOI: 10.1007/s10955-006-9185-9}, VOLUME = {}, YEAR = {2006}, %NUMBER = {}, PAGES = {21}, }

@inbook{FleigeHassiSnooWinkler2006, author = {Fleige, A. and Hassi, S. and de Snoo, H.S.V. and Winkler, H.}, title = {Generalized Friedrichs extensions associated with interface conditions for Sturm-Liouville operators}, pages = {135--145}, volume = {163}, publisher= {Oper. Theory Adv. Appl.}, %editor = {}, year = {2006} }

@article {GambaudoMartens2006,

AUTHOR = {Gambaudo, J.M. and Martens, M. }, TITLE = {Algebraic Topoloty for Minimal Cantor Sets}, JOURNAL = {Ann. Inst. Henri Poincar{\'e}}, VOLUME = {7}, YEAR = {2006}, NUMBER = {3}, PAGES = {423--446}, }

@article{HassiSnooSterkWinkler2006, author = {Hassi, S. and de Snoo, H.S.V. and Sterk, A.E. and Winkler, H.}, title = {Non-standard boundary conditions for a class of Sturm-Liouville problems}, journal = {Revue Roumaine de Mathematiques Pures et Appliquees}, volume = {51}, year = {2006}, issue = {5, 6}, pages = {641--653} }

@article {HassiMollerSnoo2006,

AUTHOR = {Hassi, S. and M{\"o}ller, M. and de Snoo, H.S.V.}, TITLE = {A class of Nevanlinna functions associated with Sturm-Liouville operators}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {134}, YEAR = {2006}, NUMBER = {}, PAGES = {2885--2893}, }

@article {HassiSandoviciSnooWinkler2006,

AUTHOR = {Hassi, S. and Sandovici, A. and de Snoo, H.S.V. and Winkler, H.}, TITLE = {Form sums of nonnegative selfadjoint operators}, JOURNAL = {Acta Math. Hungar.}, VOLUME = {111}, YEAR = {2006}, NUMBER = {}, PAGES = {81--105}, }

@article {KaltenbackWinklerWoracek2006,

AUTHOR = {Kaltenb{\"a}ck, M. and Winkler, H. and Woracek, H.}, TITLE = {Generalized Nevanlinna functions with essentially positive spectrum}, JOURNAL = {J. Oper. Theory}, VOLUME = {55}, YEAR = {2006}, %NUMBER = {}, PAGES = {17--48}, }

@article {KulskeRedig2006,

AUTHOR = {K{\"u}lske, C. and Redig, R.}, TITLE = {Loss without recovery of Gibbsianness during diffusion of continuous spins}, JOURNAL = {Prob. Theor. Rel. Fields}, VOLUME = {135}, YEAR = {2006}, %NUMBER = {}, PAGES = {428--456}, }

@inproceedings{LabrousseSandoviciSnooWinkler2006,

AUTHOR = {Labrousse, J.-Ph. and Sandovici, A. and de Snoo, H.S.V. and Winkler, H.}, TITLE = {Quasi-Fredholm relations in Hilber spaces Universitatea din Bacau Studii si Cercetari Stiintifice}, BOOKTITLE = {Ser. Mat., Vol 16} PAGES = {93--106}, YEAR = {2006}, }

@article {Sandovici2006,

AUTHOR = {Sandovici, A.}, TITLE = {Langrangian pairs in Hilbert spaces}, JOURNAL = {Methods of Functional Analysis and Topology}, VOLUME = {12}, YEAR = {2006}, NUMBER = {1}, PAGES = {82--100}, }

@inproceedings{Sandovici2006,

AUTHOR = {Sandovici, A.}, TITLE = {Canonical regular extensions of symmetric linear relations}, BOOKTITLE = {Proc. 20th Conference in Operator Theory} PAGES = {207--221}, YEAR = {2006}, }

@PHDTHESIS{Sandovici2006,

AUTHOR = {Sandovici, A.}, TITLE = {Contributions to the extension theory in Hilbert spaces}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = {Faculty of Mathematics and Natural Sciences}, MONTH = {June}, YEAR = {2006}, NOTE = {Promotor: H.S.V. de Snoo, 205 pages}, }

2005

@article {ArlinskiHassiSnoo2005,

```
AUTHOR = {Arlinski{\u\i} , Yu.M. and Hassi, S. and de Snoo, H.S.V.},
TITLE = {$Q$-functions of Hermitian contractions of Kre\u{\i}n-Ovcharenko type },
JOURNAL = {Integral Equations Operator Theory},
VOLUME = {35},
YEAR = {2005},
PAGES = {153-189},
```

}

@article {BroerHanssmannYou2005,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. and You, J.}, TITLE ={Bifurcations of normally parabolic tori in Hamiltonian systems }, JOURNAL = {Nonlinearity}, VOLUME = {18}, YEAR = {2005}, PAGES = {1735-1769},

}

@article {BroerNaudotRoussarieSaleh2005,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R. and Saleh, K.}, TITLE ={Bifurcations of a predator-prey model with non-monotonic response function}, JOURNAL = {C.R. Acad. Sci. Paris}, VOLUME = {341}, YEAR = {2005}, NUMBER = {1}, PAGES = {601-604},

}

@article {HassiSebestyenSnoo2005,

AUTHOR = {Hassi, S. and Sebesty\'en, Z. and de Snoo, H.S.V.}, TITLE ={On the nonnegativity of operator products}, JOURNAL = {Acta Math. Hungar.}, VOLUME = {109}, YEAR = {2005}, NUMBER = {4}, PAGES = {1-15},

}

@article {KaltenbackWinklerWoracek2005,

AUTHOR = { Kaltenb\"ack, M. and Winkler, H. and Woracek, H.}, TITLE ={Almost Pontryagin spaces}, JOURNAL = {Oper. Theory Adv. Appl.}, VOLUME = {160}, YEAR = {2005}, PAGES = {253-273},

}

@article {KulskeRedig2005,

AUTHOR = {K\"ulske, C. and Redig, F.}, TITLE ={Loss without recovery of Gibbsianness during diffusion of continuous spins}, JOURNAL = {Probability Theory and Related Fields}, YEAR = {2005}, PAGES = { Online First, DOI:

10.1007/s00440-005-0469-9}, }

@article {LiveraniMartens2005,

AUTHOR = {Liverani, C. and Martens, M.}, TITLE ={Convergence to equilibrium for intermittent symplectic maps}, JOURNAL = {Commun. Math. Phys.}, VOLUME = {260}, YEAR = {2005}, NUMBER = {3}, PAGES = { 527-556},

}

@article {MartensNaudotYang2005,

AUTHOR = {Martens, M. and Naudot, V. and Yang, J.}, TITLE ={Suspended Cubic H\'enon like

map in the unfolding of a degenerate homoclinic orbit with a resonance},

JOURNAL = {C.R. Acad. Sci. Paris}, VOLUME = {340}, YEAR = {2005}, NUMBER = {1}, PAGES = {843-846},

}

@article {MocanuSandovici2005,

AUTHOR = {Mocanu, M. and Sandovici, A.}, TITLE ={On the convergence of a sequence generated by an integral}, JOURNAL = {Creative Mathematics}, VOLUME = {14}, YEAR = {2005}, PAGES = {31-42},

}

@article {NaudotNeirrynck2005,

AUTHOR = {Naudot, V. and Neirynck, K.}, TITLE ={ Poincar\'e return map near a planar center}, JOURNAL = {Communications on Applied Nonlinear Analysis}, VOLUME = {12}, YEAR = {2005}, NUMBER = {3}, PAGES = {1-27},

}

@article {Sandovici2005,

AUTHOR = {Sandovici, A.}, TITLE ={A smooth Gauge model on tangent bundle}, JOURNAL = {Rendiconti del Seminario Matematico Torino}, VOLUME = {63}, YEAR = {2005}, NUMBER = {3}, PAGES = {255-282},

}

@article {SandoviciSnooWinkler2005,

AUTHOR = {Sandovici, A. and de Snoo, H.S.V. and Winkler, H.}, TITLE ={The structure of linear relations in Euclidean spaces}, JOURNAL = {Lin. Alg. Appl.}, VOLUME = {397}, YEAR = {2005}, %NUMBER = {}, PAGES = {141-169},

}

@article {SandoviciBlanuta2005,

AUTHOR = {Sandovici, A. and Blanuta, V.}, TITLE ={Generalized Beil metric on Cartan spaces}, JOURNAL = {Tensor (N.S.)}, VOLUME = {66}, YEAR = {2005}, NUMBER = {1}, PAGES = {34-43},

}

@article {SnooWinkler2005,

AUTHOR = {De Snoo, H.S.V. and Winkler, H.}, TITLE ={Two-dimensional trace-normed canonical system of differential equations and selfadjoint interface conditions}, JOURNAL = {Integral Equations Operator Theory}, VOLUME = {51}, YEAR = {2005}, PAGES = {73-108},

}

@article {SnooWinkler2005,

AUTHOR = {De Snoo, H.S.V. and Winkler, H.}, TITLE ={Canonical systems of differential equations with selfadjoint interface conditions on graphs}, JOURNAL = {Proc. Roy. Soc. Edinburgh}, VOLUME = {135A}, YEAR = {2005}, PAGES = {297-315},

}

@article {CiocciLitvakHinenzonBroer2005,

AUTHOR = {Ciocci, M.C. and Litvak-Hinenzon, A. and Broer, H.W.}, TITLE ={Survey on dissipative {\sc kam} theory including quasi-periodic bifurcation

theory based on lectures by Henk Broer},

JOURNAL = {Geometric Mechanics and Symmetry: the

Peyresq Lectures},

VOLUME = {306}, YEAR = {2005}, PAGES = {303-355},

}

@article {DumortierBroerMawhinVanderbauwhedeVerduynLunel2005,

AUTHOR = {Durmortier, F. and Broer, H.W. and Mawhin, J. and Vanderbauwhede, A. and Verduyn-Lunel, S.M.}, TITLE ={ Equadiff 2003, Proc. Int. Conf. Differential Equations}, JOURNAL = {Proc. Int. Conf. Differential Equations}, YEAR = {2005}, PAGES = {1159},

}

@article {Efstathiou2005,

AUTHOR = {Efstathiou, K.}, TITLE ={Metamorphoses of Hamiltonian Systems with Symmetries}, JOURNAL = {LNM 1864}, YEAR = {2005}, PAGES = {149},

}

@inproceedings{BovierKulske2005,

AUTHOR = {Bovier, A. and K\ülske, Ch.}, TITLE = {Coarse graining techniques for (random) Kac models}, BOOKTITLE = {Interacting Stochastic Systems}, PAGES = {11--28}, YEAR = {2005},

}

@inproceedings{BroerCushmanFasso2005,

AUTHOR = {Broer, H.W. and Cushman, R.H. and Fass{\'o}, F.}, TITLE = {A Hamiltonian KAM Theorem for Bundles of Lagrangean Tori}, BOOKTITLE = {Equadiff 2003, Proc. Int. Conf. Differential Equations}, PAGES = {696--701}, YEAR = {2005},

}

@inproceedings{BroerHanssmannJorbaVillanuevaWagener2005,

AUTHOR = {Broer, H.W. and Han{\ss}mann, H. and Jorba, A. and Villanueva, J. and Wagener, F.O.O..}, TITLE = {Quasi-periodic response solutions at normal-internal resonances}, BOOKTITLE = {Equadiff 2003, Proc. Int. Conf. Differential Equations}, PAGES = {702--707}, YEAR = {2005},

}

@inproceedings{BroerHooNaudot2005,

```
AUTHOR = {Broer, H.W. and Hoo, J and Naudot, V.},
TITLE = {Normal Linear stability of Quasi-Periodic Tori in the Hamiltonian $1:-1$ resonance case},
BOOKTITLE = {Equadiff 2003, Proc. Int. Conf. Differential Equations},
PAGES = {708--713},
YEAR = {2005},
```

}

@inproceedings{BroerNaudotRoussarie2005,

AUTHOR = {Broer, H.W. and Naudot, V. and Roussarie, R.}, TITLE = {Extension of catastrophe theory to Dulac unfoldings}, BOOKTITLE = {Equadiff 2003, Proc. Int. Conf. Differential Equations}, PAGES = {714--719}, YEAR = {2005},

}

@inproceedings{BroerSimoVitolo2005,

AUTHOR = {Broer, H.W. and Sim{\'o}, C. and Vitolo, R.}, TITLE = {Quasi-periodic H{\'e}non-like strange attractors in the Lorenz-84 climate model

with seasonal forcing},

BOOKTITLE = { Equadiff 2003, Proc. Int. Conf. Differential Equations}, PAGES = {601--606}, YEAR = {2005},

}

@inproceedings{BroerNoortSimo2005,

AUTHOR = {Broer, H.W. and Van Noort, M. and Sim{\'o}, C.}, TITLE = {Existence and measure of invariant tori in Hamiltonian one-and-a-half degree of freedom systems}, BOOKTITLE = {Equadiff 2003, Proc. Int. Conf. Differential Equations}, PAGES = {595--600}, YEAR = {2005},

}

@inproceedings{Broer2005,

AUTHOR = {Broer, H.W.}, TITLE = {Quasi-periodicity in dissipative and conservative systems}, BOOKTITLE = {Proc. Symposium Henri Poincar{\'e} }, YEAR = {2005},

}

@inproceedings{DerkachHassiMalamudSnoo2005,

AUTHOR = {Derkach, V.A. and Hassi, S. and Malamud, M.M. and de Snoo, H.S.V.}, TITLE = {Boundary relations and orthogonal coupling of symmetric operators}, BOOKTITLE = {Proc. Algorithmic Information Theory Conference}, PAGES = {41-56}, YEAR = {2005},

}

@inproceedings{HassiSandoviciSnooWinkler2005,

AUTHOR = {Hassi, S. and Sandovici, A. and de Snoo, H.S.V. and Winkler, H.}, TITLE = {Extremal extensions of nonnegative linear relations}, BOOKTITLE = {Proc. Algorithmic Information Theory Conf.}, PAGES = {57-66}, YEAR = {2005},

}

@inproceedings{IftimeSandoviciGolo2005,

AUTHOR = {Iftime, O.V. and Sandovici, A. and Golo, G.}, TITLE = {Tools for analysis of Dirac Structures on Banach Spaces}, BOOKTITLE = {Proc. 44th IEEE Conf. Decision and Control and European Controle Conf.}, PAGES = {6 pages}, YEAR = {2005},

}

@inproceedings{SandoviciSnooWinkler2005,

AUTHOR = {Sandovici, A. and de Snoo, H.S.V. and Winkler, H.}, TITLE = {Ascent, descent, nullity, and defect for linear relations}, BOOKTITLE = {Proc. Algorithmic Information Theory Conf.}, PAGES = {177--184}, YEAR = {2005},

}

@PHDTHESIS{Hoo2005,

AUTHOR = {Hoo, J.}, TITLE = {Quasi-periodic bifurcations in a strong resonance: combination tones in gyroscopic stabilisation}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = { Faculty of Mathematics and Natural Sciences, University of Groningen }, MONTH = {January}, YEAR = {2005}, NOTE = {Advisors: H.W. Broer, 169 pages},

}

@PHDTHESIS{Gulikers2005,

AUTHOR = {Gulikers, I.}, TITLE = {Reinvention of geometry}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = { Faculty of Mathematics and Natural Sciences, University of Groningen }, MONTH = {December}, YEAR = {2005}, NOTE = {Advisors: H.W. Broer, A. van Streun, J.A. van Maanen 270 pages},

}

@PHDTHESIS{Saleh2005,

AUTHOR = {Saleh, K.}, TITLE = {Organising centres in the semi-global analysis of dynamical systems}, SCHOOL = {University of Groningen}, TYPE = {PhD Dissertation}, ADDRESS = { Faculty of Mathematics and Natural Sciences, University of Groningen }, MONTH = {December}, YEAR = {2005}, NOTE = {Advisors: H.W. Broer, 133 pages},

}

2004

@article {Broer2004,

AUTHOR = {Broer, H.W.}, TITLE = { Kolmogorov la `K' de KAM}, JOURNAL = { Butllet{\'i} de la Societat Catalana de Matematiques }, VOLUME = {18}, YEAR = {2004}, NUMBER = {2}, PAGES = {39--57}

}

@article {Broer2004b,

AUTHOR = {Broer, H.W.}, TITLE = {KAM theory: the legacy of Kolmogorov’s 1954 paper}, JOURNAL = {Bull. Amer. Math. Soc. (New Series) }, VOLUME = {41}, YEAR = {2004}, NUMBER = {4}, PAGES = {507--521}

}

@article {BroerHoveijnNoortSimoVegter2004,

```
AUTHOR = {Broer, H.W. and Van Noort, M. and Sim{\'o}, C. and Vegter, G.},
TITLE = { The parametrically forced pendulum: a case study in $1\frac{1}{2}$ degree of freedom },
JOURNAL = { J. Dynamics and Differential Equations },
VOLUME = {16},
YEAR = {2004},
NUMBER = {4},
PAGES = {897—947}
```

}

@article {DerkachHassiMalamudSnoo2004,

AUTHOR = {Derkach, V.A. and Hassi, S. and Malamud, M.M. and De Snoo, H.S.V..}, TITLE = { Boundary relations and Weyl families}, JOURNAL = { Rus. Doklady Acad. Sci. }, VOLUME = {399}, YEAR = {2004}, PAGES = {151—156}

}

@article {Hagen2004,

AUTHOR = {Hagen, A.}, TITLE = {Hyperbolic trajectories of time discretizations}, JOURNAL = {Nonlinear Analysis}, VOLUME = {59}, YEAR = {2004}, PAGES = {121—132}

}

@article {HassiMalamudSnoo2004,

AUTHOR = {Hassi, S. and Malamud, M.M. and De Snoo, H.S.V..}, TITLE = { On Kre\u{\i}n's extension theory of nonnegative operators }, JOURNAL = {Math. Nachr.}, VOLUME = {274/275}, YEAR = {2004}, PAGES = {40—73}

}

@article {HassiSnooTsekanovskiui2004,

AUTHOR = {Hassi, S. and De Snoo, H.S.V. and Tsekanovski\u{\i}, E.R..}, TITLE = { The realization problem for Herglotz-Nevanlinna functions}, JOURNAL = {Unsolved problems in mathematical systems and control theory}, YEAR = {2004}, PAGES = {8—13}

}

@article {HassiMollerSnoo2004,

AUTHOR = {Hassi, S. and M{\"o}ller, M. and De Snoo, H.S.V. }, TITLE = {Singular Sturm-Liouville equations whose coefficients depend rationally on the eigenvalue parameter}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {295}, YEAR = {2004}, PAGES = {258—275}

}

@article {Sandovici2004,

AUTHOR = {Sandovici, A. }, TITLE = {Two remarkable connections associated with a Beil metric on Cartan spaces}, JOURNAL = {Rad. Mat.}, VOLUME = {12}, YEAR = {2004}, PAGES = {189—203}

}

@article {SandoviciBlanuta2004,

```
AUTHOR = {Sandovici, A. and Blanuta, V. },
TITLE = { On a framed $f$-structure on tangent manifold of a Riemannian space},
JOURNAL = {Libertas Math.},
VOLUME = {24},
YEAR = {2004},
PAGES = {21—28}
```

}

@article {Broer2004,

AUTHOR = {Broer, H.W. }, TITLE = {Ken uw klassieken: Kolmogorov in het Concertgebouw}, JOURNAL = {Nederlands Tijdschrift voor Natuurkunde}, VOLUME = {jaargang 70}, YEAR = {2004}, PAGES = {20—21}

}

@article {Broer2004,

AUTHOR = {Broer, H.W. }, TITLE = {An interview with Jacob Palis}, JOURNAL = {Dynamical Systems Magizine}, YEAR = {2004},

}

@inproceedings{DerkachHassiSnoo2004,

AUTHOR = {Derkach, V.A. and Hassi, S. and De Snoo, H.S.V.}, TITLE = {Singular perturbations as range perturbations in a Pontryagin space}, BOOKTITLE = {Oper. Theory: Adv. Appl., volume 154}, PAGES = {51--68}, YEAR = {2004}

}

@inproceedings{SandoviciBlanuta2004,

AUTHOR = {Sandovici, A. and Blanuta, V.}, TITLE = {Beil metrics on Cartan spaces}, BOOKTITLE = {Recent advances in geometry and topology}, PAGES = {353--363}, YEAR = {2004}

}

@inproceedings{Winkler2004, AUTHOR = {Winkler, H.}, TITLE = {Inverse problems for small perturbations of canonical systems}, BOOKTITLE = {Proc. MTNS 2004}, PAGES = {3 pages}, YEAR = {2004}

}