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Publications by Henk W. Broer

H. W. Broer (2017) Near the Horizon: An Invitation to Geometric Optics. The Carus Mathematical Monographs (MAA), 2017.   bib
H.W. Broer. Laudatie voor John Mather (Uitreiking Brouwermedaillie 2014). Nieuw Archief voor Wiskunde 5/17:19-20, 2016.   bib
H.W. Broer. Laudatie voor Marius Crainic (Award ceremony N.G. de Bruin Prize). Nieuw Archief voor Wiskunde 5/17:105-106, 2016.   bib
H.W. Broer. Alles beweegt, maar waarheen? Nieuw Archief voor Wiskunde 5/17:128-136, 2016.   bib
Henk W. Broer and Heinz Hanßmann. On Jupiter and his Galilean satellites: Librations of De Sitter’s periodic motions. Indagationes Mathematicae, 27(5):1305 – 1336, 2016. Dynamics and Geometry.   doi

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H. W. Broer and L. Zhao. De Sitter’s theory of Galilean satellites. Celestial Mechanics and Dynamical Astronomy, 2016.   doi
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H. Jardón Kojakhmetov, H.W. Broer, and R. Roussarie. Analysis of a slow–fast system near a cusp singularity. Journal of Differential Equations, 260(4):3785–3843, 2016.   url
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H. W. Broer. Near-Horizon Celestial Phenomena, a Study in Geometric Optics. Acta Applicandae Mathematicae, 137:17–39, 2015.   url
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W. Broer, H. Waalkens, V.B. Svetovoy, J. Knoester, and G. Palasantzas. Nonlinear actuation dynamics of Casimir oscillators in the presence of surface roughness. Phys. Rev. Applied, 4:054016, 2015.   url
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Konstantinos Efstathiou, Xia Liu, and Henk W. Broer. The Boundary-Hopf-Fold Bifurcation in Filippov Systems. SIAM Journal on Applied Dynamical Systems, 14(2):914–941, 2015.   url
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H. W. Broer. Review of ’Henri Poincaré: a scientific biography’ by Jeremy Gray. BSHM Bulletin: Journal of the British Society for the History of Mathematics 29:1, 77-79, 2014.   url
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H. W. Broer. Bernoulli’s Light Ray Solution of the Brachistochrone Problem Through Hamilton’s Eyes. Int. J. Bifurcations Chaos, 24:1440009, 2014.   url
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Ü. Çiftçi, H. Waalkens, and H. W. Broer. Cotangent bundle reduction and Poincaré-Birkhoff normal forms. Physica D, 268:1–13, 2014.   url
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H. Jardón-Kojakhmetov and Henk W. Broer. Polynomial normal forms of constrained differential equations with three parameters. Journal of Differential Equations, 257(4):1012–1055, 2014.   url
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H. W. Broer (2013) Hemelverschijnselen nabij de Horizon. Epsilon Uitgaven, 2013.   bib
H. W. Broer. Bernoulli’s lichtstraal-oplossing van het brachistochrone probleem door de ogen van Hamilton. Nieuw Archief voor Wiskunde 5th series, 14(2):99–107, 2013.   url
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H.W. Broer, H. Hanßmann, and Y. You. On the destruction of resonant Lagrangean tori in Hamiltonian systems. In A. Johann, H.-P. Kruse, F. Rupp, and S. Schmitz, eds., Recent Trends in Dynamical Systems, Proceedings of a Conference in Honor of Jürgen Scheurle. Heidelberg, Springer, Ch. 13, 2013.   url
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H. W. Broer, T. J. Kaper, and M. Krupa. Geometric Desingularization of a Cusp Singularity in Slow–Fast Systems with Applications to Zeeman’s Examples. J. Dyn. Diff. Equat., 25:925–958, 2013.   url
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H. W. Broer, M. Levi, and C. Simó. Large scale radial stability density of Hill’s equation. Nonlinearity, 26:565–589, 2013.   url
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H.W. Broer and G. Vegter. Resonance and singularities. In S. Ibáñez, J.S. Pérez del Río, A. Pumariño, and J.Á. Rodríguez, eds., Progress and Challenges in Dynamical Systems. Heidelberg, Springer, pages 89–126, 2013.   url
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K. Efstathiou and H. W. Broer. Uncovering Fractional Monodromy. Comm. Math. Phys., 324:549–588, 2013.   url
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A.E. Sterk, R. Vitolo, and H.W. Broer. Het onvoorspelbare venijn van de staart. Nieuw Archief voor Wiskunde 5th series, 14(3):164-167, 2013.   url
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H.W. Broer. Perspectives on the legacy of Poincaré in the field of dynamical systems. NAW, 5/13(3):201–208, 2012.   url
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H.W. Broer. Resonance and Fractal Geometry. Acta Applicandae Mathematicae, 120(1):61–86, 2012.   url
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A. Sterk, M.P. Holland, P. Rabassa, H.W. Broer, and R. Vitolo. Predictability of extreme values in geophysical models. Nonlin. Processes Geophys., 19:529–539, 2012.   url
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D.G.M. Beersma, H.W. Broer, K. Efstathiou, K.A. Gargar, and I. Hoveijn. Pacer cell response to periodic Zeitgebers. Physica D, 19:1516–1527, 2011.   url
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H. Broer, H. Dijkstra, C. Simó, A. Sterk, and R. Vitolo. The dynamics of a low-order model for Atlantic Multidecadal Oscillation. DCDS-B, 16(1):73–102, 2011.   url
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H.W. Broer and F. Takens (2011) Dynamical Systems and Chaos. Springer, 2011.   url
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H. W. Broer, S. J. Holtman, G. Vegter, and R. Vitolo. Dynamics and Geometry Near Resonant Bifurcations. Regular and Chaotic Dynamics, 16(1-2):39–50, 2011.   url
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M. P. Holland, R. Vitolo, P. Rabassa, A. E. Sterk, and H. W. Broer. Extreme value laws in dynamical systems under physical observables. Physica D, 2011.   url
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R. Vitolo, H. Broer, and C. Simó. Quasi-periodic Bifurcations of Invariant Circles in Low-dimensional Dissipative Dynamical Systems. Regular and Chaotic Dynamics, 16(1-2):154–184, 2011.   url
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H.W. Broer. Do Diophantine vectors form a Cantor bouquet? Journ. Difference Equations and Applications, 16(5/6):433–434, 2010.   url
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H. W. Broer, K. Efstathiou, and O. V. Lukina. A geometric fractional monodromy. DCDS-S, 3(4):517–532, 2010.   url
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H. W. Broer and V. A. Gaiko. Global qualitative analysis of a quartic ecological model. Nonlinear Anal., 72(2):628–634, 2010.   url
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H. W. Broer, H. Hanßmann, and M. B. Sevryuk (eds.). Special Issue on KAM Theory and its applications.. DCDS-S, 3(4), 2010.   url
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H.W. Broer, B. Haselblatt, and F. Takens (eds.) (2010) Handbook of Dynamical Systems, Vol. 3. North-Holland, 2010.   url
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H. W. Broer, S.J. Holtman, and G. Vegter. Recognition of resonance type in periodically forced oscillators. Physica D, 239(17):1627–1636, 2010.   bib
H.W. Broer and M.B. Sevryuk. KAM Theory: quasi-periodicity in dynamical systems. In H.W. Broer, B. Hasselblatt, and F. Takens, eds., Handbook of Dynamical Systems. North-Holland, pages 249–344, 2010.   url
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H. W. Broer, C. Simó, and R. Vitolo. Chaos and quasi-periodicity in diffeomorphisms of the solid torus. DCDS-B, 14(3):871–905, 2010.   url
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H.W. Broer and F. Takens. Preliminaries in Dynamical Systems Theory. In H.W. Broer, B. Hasselblatt, and F. Takens, eds., Handbook of Dynamical Systems. North-Holland, pages 1–42, 2010.   url
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A.E. Sterk, R. Vitolo, H.W. Broer, Simó , and H.A. Dijkstra. New nonlinear mechanisms of midlatitude atmospheric low-frequency variability. Physica D, 239(10):702–718, 2010.   url
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R. Vitolo, H.W. Broer, and C. Simó. Routes to chaos in the Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms. Nonlinearity, 23:1919–1947, 2010.   url
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H.W. Broer. Normal Forms in Perturbation Theory. In Encyclopedia of Complexity and Systems Science. Springer, 2009.   url
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H.W. Broer, M.C. Ciocci, H. Hanßmann, and A. Vanderbauwhede. Quasi-periodic stability of normally resonant tori. Physica D, 238:309–318, 2009.   url
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H.W. Broer and H. Hanßmann. Hamiltonian Perturbation Theory (and Transition to Chaos). In Encyclopedia of Complexity and Systems Science. Springer, 2009.   url
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H.W. Broer, S.J. Holtman, G. Vegter, and R. Vitolo. Geometry and dynamics of mildly degenerate Hopf-Neimarck-Sacker families near resonance. Nonlinearity, 22:2161–2200, 2009.   url
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H.W. Broer and F. Takens (2009) Dynamical Systems and Chaos. Epsilon Uitgaven, 2009.   bib
V.A. Gaiko, H.W. Broer, and W.T. van Horsen. Limit cycles of a population dynamics model. In Proceedings of 4th International Scientific Conference on Physics and Control (PHYSCON 2009), September 2009, Catania, Italy. Pages 1922–1925, 2009.   url
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H.W. Broer, K. Efstathiou, and E. Subramanian. Robustness of unstable attractors in arbitrarily sized pulse-coupled systems with delay. Nonlinearity, 21:13–49, 2008.   bib
H.W. Broer, K. Efstathiou, and E. Subramanian. Heteroclinic cycles between unstable attractors. Nonlinearity, 21:1385–1410, 2008.   bib
H.W. Broer, S.J. Holtman, and G. Vegter. Recognition of the bifurcation type of resonance in mildly degenerate Hopf-Neimark-Sacker families. Nonlinearity, 21:2463–2482, 2008.   bib
H.W. Broer, C. Simó, and R. Vitolo. The Hopf-Saddle-Node bifurcation for fixed points of 3D-diffeomorphisms, analysis of a resonance ‘bubble’. Physica D, 237:1773–1799, 2008.   bib
H.W. Broer, C. Simó, and R. Vitolo. The Hopf-Saddle-Node bifurcation for fixed points of 3D-diffeomorphisms, the Arnol’d resonance web. Bull. Belgian Math. Soc. Simon Stevin, 15:769–787, 2008.   bib
H.W. Broer and G. Vegter. Generic Hopf-Ne\u\imark-Sacker bifurcations in feed forward systems. Nonlinearity, 21:1547–1578, 2008.   bib
H.W. Broer and R. Vitolo. Dynamical systems modeling of low-frequency variability in low-order atmospheric models. Discrete and Continous Dynamical Systems - Series B, 10(2/3):401–419, 2008.   bib
O.V. Lukina, F. Takens, and H.W. Broer. Global properties of integrable Hamiltonian systems. Regular and Chaotic Dynamics, 13(6):588–630, 2008.   bib
H.W. Broer. Computergebruik en demathematisering. Nieuw Arch. Wisk. 5th series, 5(3):201–206, 2007.   bib
H.W. Broer, M.C. Ciocci, and H. Hanßmann. The quasi-periodic reversible Hopf bifurcation. IJBC, 17(8):2605–2623, 2007.   bib
H.W. Broer, R.H. Cushman, F. Fassó, and F. Takens. Geometry of \sc kam tori for nearly integrable Hamiltonian systems. Ergod. Th. &Dynam. Sys., 27:725–741, 2007.   bib
H.W. Broer, R. Van Dijk, and R. Vitolo. Survey of strong normal-interenal $k:\ell$ resonances in quasi-periodically driven oscillators for $\ell = 1,2,3.$. In Symmetry and Perturbation Theory, Proc. Int. Conf. SPT. Pages 45–55, 2007.   bib
H.W. Broer, M. Golubitsky, and G. Vegter. Geometry of resonance tongues. In Singularity Theory, Proc. 2005 Marseille Singularity School and Conference,dedicated to Jean-Paul Brasselet on His 60th Birthday. Pages 327–356, 2007.   bib
H.W. Broer, A. Hagen, and G. Vegter. Numerical continuation of normally hyperbolic invariant manifolds. Nonlinearity, 20:1499–1534, 2007.   bib
H.W. Broer, H. Hanßmann, and J. Hoo. The quasi-periodic Hamiltonian Hopf bifurcations. Nonlinearity, 20:417–460, 2007.   bib
H.W. Broer, J. Hoo, and V. Naudot. Normal linear stability of quasi-periodic tori. J. Diff. Eqns., 232(2):355–418, 2007.   bib
H.W. Broer, V. Naudot, R. Roussarie, and K. Saleh. Dynamics of a predator-prey model with non-monotonic response function. DCDS, 18(2&3):221–251, 2007.   bib
H.W. Broer, V. Naudot, R. Roussarie, K. Saleh, and F.O.O. Wagener. Organising centres in the semi-global analysis of dynamical systems. IJAMAS, 12(D07):7–36, 2007.   bib
H.W. Broer and F. Takens. Unicity of \sc kam tori. Ergod. Th. &Dynam. Sys., 27:713–724, 2007.   bib
R. Vitolo, H.W. Broer, and C. Simó. The Hopf-saddle-node for fixed points of 3d-diffeomorphisms. In Symmetry and Perturbation Theory, Proc. Int. Conf. SPT. Pages 280–281, 2007.   bib
H.W. Broer, H. Hanßmann, J. Hoo, and V. Naudot. Nearly-integrable perturbations of the Lagrange top: applicationsof \sc kam theory. In Dynamics and Stochastics Festschrift in Honor of M.S. Keane, Lecture Notes – Monograph Series, Vol 48. Pages 286–303, 2006.   bib
H.W. Broer, A. Hagen, and G. Vegter. A versatile algorithm for computing invariant manifolds. In Model Reduction and Coars-Graining Approaching for Multiscale Phenomena. Pages 17–38, 2006.   bib
H.W. Broer, H. Hansßmann, and J. You. Umbilical torus bifurcations in Hamiltonian systems. J. Diff. Eqns., 222:233–262, 2006.   bib
H.W. Broer, V. Naudot, R. Roussarie, and K. Saleh. A predator-prey model with non-monotonic response function. Regular and Chaotic Dynamics, 11(2):155–165, 2006.   bib
H.W. Broer, V. Naudot, and R. Roussarie. Catastrophe theory in Dulac unfoldings. Ergod. Th. &Dynam. Sys., 26:1–35, 2006.   bib
H.W. Broer. Wiskunde als kritische succesfactor? Euclides, 81(6):282–285, 2006.   bib
H.W. Broer, H. Hanßmann, and J. You. Bifurcations of normally parabolic tori in Hamiltonian systems. Nonlinearity, 18:1735–1769, 2005.   bib
H.W. Broer, V. Naudot, R. Roussarie, and K. Saleh. Bifurcations of a predator-prey model with non-monotonic response function. C.R. Acad. Sci. Paris, 341(1):601–604, 2005.   bib
M.C. Ciocci, A. Litvak-Hinenzon, and H.W. Broer. Survey on dissipative \sc kam theory including quasi-periodic bifurcationtheory based on lectures by Henk Broer. Geometric Mechanics and Symmetry: thePeyresq Lectures, 306:303–355, 2005.   bib
F. Durmortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede, and S.M. Verduyn-Lunel. Equadiff 2003, Proc. Int. Conf. Differential Equations. Proc. Int. Conf. Differential Equations, 2005.   bib
H.W. Broer, R.H. Cushman, and F. Fassó. A Hamiltonian KAM Theorem for Bundles of Lagrangean Tori. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 696–701, 2005.   bib
H.W. Broer, H. Hanßmann, A. Jorba, J. Villanueva, and F.O.O. Wagener. Quasi-periodic response solutions at normal-internal resonances. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 702–707, 2005.   bib
H.W. Broer, J Hoo, and V. Naudot. Normal Linear stability of Quasi-Periodic Tori in the Hamiltonian $1:-1$ resonance case. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 708–713, 2005.   bib
H.W. Broer, V. Naudot, and R. Roussarie. Extension of catastrophe theory to Dulac unfoldings. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 714–719, 2005.   bib
H.W. Broer, C. Simó, and R. Vitolo. Quasi-periodic Hénon-like strange attractors in the Lorenz-84 climate modelwith seasonal forcing. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 601–606, 2005.   bib
H.W. Broer, M. Van Noort, and C. Simó. Existence and measure of invariant tori in Hamiltonian one-and-a-half degree of freedom systems. In Equadiff 2003, Proc. Int. Conf. Differential Equations. Pages 595–600, 2005.   bib
H.W. Broer. Quasi-periodicity in dissipative and conservative systems. In Proc. Symposium Henri Poincaré. 2005.   bib
H.W. Broer. Kolmogorov la ‘K’ de KAM. Butlletí de la Societat Catalana de Matematiques, 18(2):39–57, 2004.   bib
H.W. Broer. KAM theory: the legacy of Kolmogorov’s 1954 paper. Bull. Amer. Math. Soc. (New Series), 41(4):507–521, 2004.   bib
H.W. Broer, M. Van Noort, C. Simó, and G. Vegter. The parametrically forced pendulum: a case study in $1\frac12$ degree of freedom. J. Dynamics and Differential Equations, 16(4):897—947, 2004.   bib
H.W. Broer. Ken uw klassieken: Kolmogorov in het Concertgebouw. Nederlands Tijdschrift voor Natuurkunde, jaargang 70:20—21, 2004.   bib
H.W. Broer. An interview with Jacob Palis. Dynamical Systems Magizine, 2004.   bib