Henk Broer > DSMP > MATHS > JBI > FWN > RUG

You can also find my publications on Google Scholar and ResearchGate

Popular, Reviews, etc.

Selected books

  • With M. Seri and F. Takens, Oscillations: swings and vibrations from a mathematical point of view. To be published
  • Near the Horizon, an Invitation to Geometric Optics. MAA The Carus Mathematical Monographs 33 2016
  • Hemelverschijnselen nabij de Horizon, naar Minnaert en Wegener, Bernoulli en Hamilton. Epsilon-Uitgaven 77 2013
  • With B. Hasselbatt and F. Takens (Eds.), Handbook of Dynamical Systems Vol 3 North-Holland Elsevier 2010
  • With F. Takens, Dynamical Systems and Chaos. Epsilon-Uitgaven 64 2009; Applied Mathematical Sciences 172 Springer Verlag 2011
  • With B. Krauskopf and G. Vegter (Eds.), Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday. Institute of Physics Publishing 2001
  • Meetkunde en Fysica, met differentiaalvormen en integraalstellingen. Epsilon-Uitgaven 44 1999
  • With G.B. Huitema and M.B. Sevryuk, Quasi-periodic tori in families of dynamical systems: order amidst chaos. Lecture Notes in Mathematics 1645 Springer Verlag 1996
  • With J. van der Craats and F. Verhulst, Het einde van de voorspelbaarheid? Chaostheorie, ideeen en toepassingen. Aramith Uitgevers – Epsilon Uitgaven 35 1995; Chaostheorie – Het einde van de voorspelbaarheid? Epsilon Uitgaven 35 2003
  • With F. Dumortier, S.J. van Strien and F. Takens, Structures in Dynamics, Finite Dimensional Deterministic Studies. Studies in Mathematical Physics. North-Holland Elsevier 1991
  • With G.B. Huitema, F. Takens and B.L.J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori. Mem AMS 83(421) American Mathematical Society 1990
  • With F. Verhulst (Eds.), Dynamische systemen en chaos, een revolutie vanuit de wiskunde. Epsilon-Uitgaven 14 1990

Selected journal articles

  • With G. Vegter, Subordinate Sil’nikov bifurcations near some singularities of vector fields having low codimension. Ergod. Th. & Dynam. Sys. 4 (1984) 509-525
  • With F.M. Tangerman, From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems Ergod. Th. & Dynam. Sys. 6 (1986) 345-362
  • With B.L.J. Braaksma, On a quasi-periodic Hopf bifurcation. Ann. Institut Henri Poincaré. Analyse non linéaire 4(2) (1987) 115-168
  • With G.B. Huitema, A proof of the iso-energetic KAM-theorem from the ‘ordinary’ one. Journ. Diff. Eqns. 90(1) (1991) 52-60
  • With F. Takens, Mixed spectrum and rotational symmetry. Arch. Rational Mech. An. 124 (1993) 13-42
  • With M. Levi, Geometrical aspects of stability theory for Hill’s equations. Archive Rat. Mech. An. 131 (1995) 225-240
  • With C. Simó and J.C. Tatjer, Towards global models near homoclinic tangencies of dissipative diffeomorphisms. Nonlinearity 11(3) (1998) 667- 770
  • With F.O.O. Wagener, Quasi-periodic stability of subfamilies of an unfolded skew Hopf bifurcation. Archive Rat. Mech. An. 152 (2000) 283-326
  • With C. Simó, Resonance tongues in Hill’s equations: a geometric approach. Journ. Diff. Eqns. 166 (2000) 290-327
  • With C. Simó, Reducible linear quasi-periodic systems with positive Lyapunov exponent and varying rotation number. Journ. Diff. Eqns. 168 (2000) 60-66
  • With C. Simo and J. Puig, Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation. Commun. Math. Phys. 241 (2003) 467-503
  • KAM theory: the legacy of Kolmogorov’s 1954 paper. Bull. AMS (New Series) 41(4) (2004) 507-521
  • With V. Naudot and R.Roussarie, Catastrophe theory in Dulac unfoldings. Ergod. Th. & Dynam. Sys. 26 (2006) 1-35
  • With F. Takens, Unicity of KAM tori. Ergod. Th. & Dynam. Sys. 27 (2007) 713-724
  • With R.H. Cushman, F. Fasso and F. Takens, Geometry of KAM tori for nearly integrable Hamiltonian systems. Ergod. Th. & Dynam. Sys. 27 (2007) 725-741
  • With J. Hoo and V. Naudot, Normal linear stability of quasi-periodic tori. Journ. Diff. Eqns. 232(2) (2007) 355-418
  • With H. Hanßmann and J. Hoo, The quasi-periodic Hamiltonian Hopf bifurcations. Nonlinearity 20 (2007) 417-460
  • With G. Vegter, Generic Hopf-Neimark-Sacker bifurcations in feed forward systems. Nonlinearity 21 (2008) 1547-1578
  • With C. Simó and R. Vitolo, Chaos and quasi-periodicity in diffeomorphisms of the solid torus. DCDS-B 14(3) (2010) 871-905
  • With D.G.M. Beersma, K. Efstathiou, K.A. Gargar and I. Hoveijn, Pacer cell response to periodic Zeitgebers. Physica D 19 (2011) 1516-1527
  • Resonance and fractal geometry. Acta Applicandæ Mathematicæ 120(1) (2012) 61-86
  • With K. Efstathiou, Uncovering fractional monodromy. Comm. Math. Phys. 324 (2013) 549-588
  • With H. Hanßmann, On Jupiter and his Galilean satellites: librations of De Sitter’s periodic motions. Indag Math NS 27(5) (2016) 1305-1337
  • With N. Martynchuk and K. Efstathiou, Hamiltonian Monodromy and Morse theory. Communications in Mathematical Physics 375 (2020) 1373-1392