Henk Broer

Search results

• 2022

  Bifurcation analysis of the Topp model

  Gaiko, V. A., Sterk, A. E. & Broer, H. W., 2022, Current Trends in Analysis, its Applications and Computation. Cerejeiras, P., Reissig, M., Sabadini, I. & Toft, J. (eds.). Cham: SPRINGER BIRKHAUSER, p. 3-9 7 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

  Open Access

  File

  • Bifurcation Analysis 100%
  • Topp Model 100%
  • Limit Cycle 100%
  • Saddle-node Bifurcation 66%
  • Hopf 66%
  309 Downloads (Pure)
• 2021

  Normal resonances in a double Hopf bifurcation

  Broer, H., Hanßmann, H. & Wagener, F., Feb-2021, In: Indagationes Mathematicae. 32, 1, p. 33-54 22 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Hopf Bifurcation 100%
  • Parameter Space 50%
  • Truncation 50%
  • Perturbation Theory 50%
  • Hyperbolicity 50%
  2 Citations (Scopus)

  139 Downloads (Pure)

• Recent advances in the monodromy theory of integrable Hamiltonian systems

  Martynchuk, N., Broer, H. & Efstathiou, K., Feb-2021, In: Indagationes Mathematicae. 32, 1, p. 193-223 31 p.

  Research output: Contribution to journal › Review article › peer-review

  Open Access

  File

  • Hamiltonian Systems 100%
  • Obstruction 100%
  • Integrable System 100%
  • Open Problem 50%
  • Finite-dimensional Integrable System 25%
  2 Citations (Scopus)

  84 Downloads (Pure)
• 2020

  A Galilean dance 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons

  Broer, H. W. & Hanssmann, H., Apr-2020, In: Discrete and Continuous Dynamical Aystems. Series B. 13, 4, p. 1043-1059 17 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Phase Space 100%
  • Periodic Solution 100%
  • Parameter Space 100%
  • Hausdorff Measure 100%
  • External Parameter 100%

• Fungal tip growth arising through a codimension-1 global bifurcation

  De Jong, T. G., Sterk, A. E. & Broer, H. W., 2020, In: International Journal of Bifurcation and Chaos. 30, 7, 20 p., 2050107.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Codimension 100%
  • Global Bifurcation 100%
  • Dimensional System 66%
  • First order differential equation 66%
  • Order Differential Equation 66%
  2 Citations (Scopus)

• Hamiltonian Monodromy and Morse Theory

  Martynchuk, N., Broer, H. W. & Efstathiou, K., Apr-2020, In: Communications in Mathematical Physics. 375, 2, p. 1373–1392 20 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Hamiltonian 100%
  • Degree of Freedom 100%
  • Chern number 50%
  • Circle Action 33%
  3 Citations (Scopus)

  124 Downloads (Pure)
• 2019

  Bifurcations in Volume-Preserving Systems

  Broer, H. W. & Hanssmann, H., Aug-2019, In: Acta applicandae mathematicae. 162, 1, p. 3-32 30 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

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  • Vector Field 100%
  • Preserving System 100%
  • Volume-preserving 100%
  2 Citations (Scopus)

  103 Downloads (Pure)

• Global bifurcation analysis of Topp system

  Gaiko, V. A., Broer, H. W. & Sterk, A. E., Dec-2019, In: Cybernetics and Physics. 8, 4, p. 244–250 7 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Global Bifurcation Analysis 100%
  • Global Bifurcation 100%
  • Limit Cycle 100%
  • Quartic System 50%
  • Topp Model 50%
  1 Citation (Scopus)

  145 Downloads (Pure)
• 2018

  Persistence Properties of Normally Hyperbolic Tori

  Broer, H., Hanssmann, H. & Wagener, F., Mar-2018, In: Regular and Chaotic Dynamics. 23, 2, p. 212-225 14 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Parameter Space 100%
  • Hyperbolicity 100%
  • Dissipative System 100%
  • Conjugacy 100%
  • External Parameter 100%
  4 Citations (Scopus)

  81 Downloads (Pure)
• 2017

  De Sitter’s theory of Galilean satellites

  Broer, H. & Zhao, L., 1-Jan-2017, In: Celestial Mechanics and Dynamical Astronomy. 127, 1, p. 95-119 25 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Periodic Orbit 100%
  • Hamiltonian 100%
  • Dominates 100%
  • Positive Measure 100%
  • Orbit 100%
  8 Citations (Scopus)

  44 Downloads (Pure)
• 2016

  Analysis of a slow-fast system near a cusp singularity

  Jardon-Kojakhmetov, H., Broer, H. W. & Roussarie, R., 15-Feb-2016, In: Journal of Differential Equations. 260, 4, p. 3785-3843 59 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Fast System 100%
  • Refines 50%
  • Critical Set 50%
  • Slow Manifold 50%
  • Cusp Catastrophe 50%
  12 Citations (Scopus)

  59 Downloads (Pure)

• On Jupiter and his Galilean satellites: Librations of De Sitter's periodic motions

  Broer, H. W. & Hanssmann, H., Dec-2016, In: Indagationes mathematicae-New series. 27, 5, p. 1305-1336 32 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Motion 100%
  • Sitter 100%
  • Periodic Orbit 100%
  • Galilean Satellites 100%
  • Periodic Solution 50%
  9 Citations (Scopus)

  33 Downloads (Pure)
• 2015

  Near-Horizon Celestial Phenomena, a Study in Geometric Optics

  Broer, H. W., Jun-2015, In: Acta applicandae mathematicae. 137, 1, p. 17-39 23 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Geodesics 100%
  • Light Ray 100%
  • Planetary Atmosphere 100%
  • Optics 100%
  • Morgana 50%
  39 Downloads (Pure)

• The Boundary-Hopf-Fold Bifurcation in Filippov Systems

  Efstathiou, K., Liu, X. & Broer, H. W., 2015, In: SIAM Journal on Applied Dynamical Systems. 14, 2, p. 914-941 28 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Vector Field 100%
  • Transversals 100%
  • Phase Space 33%
  • Codimension 33%
  • Hopf Bifurcation 33%
  8 Citations (Scopus)

  299 Downloads (Pure)
• 2014

  Bernoulli's Light Ray Solution of the Brachistochrone Problem Through Hamilton's Eyes

  Broer, H. W., 2014, In: International Journal of Bifurcation and Chaos. 24, 08, 15 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  6 Citations (Scopus)

• Cotangent bundle reduction and Poincaré–Birkhoff normal forms

  Çiftçi, Ü., Waalkens, H. & Broer, H. W., 2014, In: Physica D: Nonlinear Phenomena. 268, p. 1-13 13 p.

  Research output: Contribution to journal › Article › Academic

  Open Access

  File

  • Cotangent Bundle 100%
  • Bundle Reduction 100%
  • Canonical Coordinate 100%
  • Lagrangian 50%
  • Equilateral Triangle 50%
  3 Citations (Scopus)

  426 Downloads (Pure)

• Polynomial normal forms of constrained differential equations with three parameters

  Jardon-Kojakhmetov, H. & Broer, H. W., 15-Aug-2014, In: Journal of Differential Equations. 257, 4, p. 1012-1055 44 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Differential Equation 100%
  • Polynomial 100%
  • Fast System 60%
  • Topological Equivalence 20%
  • Elliptic Umbilic 20%
  6 Citations (Scopus)

  127 Downloads (Pure)

• Preface

  Broer, H. W., Kaashoek, M. A. & Pagter, B. D., 2014, In: Indagationes Mathematicae. 25, 2, p. 163 1 p.

  Research output: Contribution to journal › Article › Academic
  24 Downloads (Pure)

• Review of 'Henri Poincare: a scientific biography' by Jeremy Gray.

  Broer, H., 2014, In: BSHM Bulletin. 29, 1, p. 77-79

  Research output: Contribution to journal › Article › Academic › peer-review
• 2013

  Bernoulli's lichtstraal-oplossing van het brachistochrone probleem door de ogen van Hamilton.

  Broer, H., 2013, In: Nieuw Archief voor Wiskunde. 14, 2, p. 99-107

  Research output: Contribution to journal › Article › Academic › peer-review

• Geometric Desingularization of a Cusp Singularity in Slow-Fast Systems with Applications to Zeeman's Examples

  Broer, H. W., Kaper, T. J. & Krupa, M., Dec-2013, In: Journal of dynamics and differential equations. 25, 4, p. 925-958 34 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Cusp Singularity 100%
  • Geometric Desingularization 100%
  • Slow-fast Systems 100%
  • Perturbation Theory 100%
  • Singular Perturbations 100%
  25 Citations (Scopus)

• Hemelverschijnselen nabij de horizon: naar Minnaert en Wegener, Bernoulli en Hamilton

  Broer, H. W., 2013, Amsterdam: Epsilon Uitgaven.

  Research output: Book/Report › Book › Academic

• Het venijn van de onvoorspelbare staart

  Sterk, A., Vitolo, R. & Broer, H., 2013, In: Nieuw Archief voor Wiskunde. 14, p. 164-167 4 p.

  Research output: Contribution to journal › Article › Popular

• Large scale radial stability density of Hill's equation

  Broer, H., Levi, M. & Simo, C., Feb-2013, In: Nonlinearity. 26, 2, p. 565-589 25 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Hill Equation 100%
  • Radial Stability 100%
  • Asymptotics 66%
  • Finer Structure 33%
  • Morse Function 33%
  5 Citations (Scopus)

• Nonlinear dynamical systems and chaos

  Broer, H. (Editor), Hoveijn, I. (Editor) & Van Gils, S. (Editor), 2013, Basel: Birkhauser.

  Research output: Book/Report › Book › Academic

• On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems

  Broer, H. W., Hanßmann, H. & You, J., 2013, Recent Trends in Dynamical Systems. Springer, p. 317-333 17 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

  4 Citations (Scopus)

• Preface

  Broer, H. W., Klop, J. W., Tijdeman, R. & Wiegerinck, J. J. O. O., 15-Nov-2013, In: Indagationes Mathematicae. 24, 4, p. 647 1 p.

  Research output: Contribution to journal › Editorial › Academic › peer-review

  Open Access

  File
  73 Downloads (Pure)

• Resonance and Singularities

  Broer, H. W. & Vegter, G., 2013, Progress and Challenges in Dynamical Systems. Springer, p. 89-126 38 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

• Uncovering Fractional Monodromy

  Efstathiou, K. & Broer, H. W., Dec-2013, In: Communications in Mathematical Physics. 324, 2, p. 549-588 40 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Monodromy 100%
  • Fibration 100%
  • Hamiltonian Systems 50%
  • Branched Covering 37%
  • Singular Fiber 25%
  9 Citations (Scopus)

  211 Downloads (Pure)
• 2012

  Extreme value laws in dynamical systems under physical observables

  Holland, M. P., Vitolo, R., Rabassa, P., Sterk, A. E. & Broer, H., 1-Mar-2012, In: Physica D: Nonlinear Phenomena. 241, 5, p. 497-513 17 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Limit Laws 100%
  • Extreme Value Laws 100%
  • Physical Observable 100%
  • Dynamical System 100%
  • Extreme Value 100%
  32 Citations (Scopus)

  357 Downloads (Pure)

• Perspectives on the legacy of Poincaré in the field of dynamical sytems

  Broer, H., 2012, In: Nieuw Srchief voor Wiskunde. 13, 3

  Research output: Contribution to journal › Article › Academic › peer-review

• Predictability of extreme values in geophysical models

  Sterk, A. E., Holland, M. P., Rabassa, P., Broer, H. W. & Vitolo, R., 2012, In: Nonlinear processes in geophysics. 19, 5, p. 529-539 11 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Observables 100%
  • Finite Time 100%
  • Extreme Value 100%
  • Geophysical Modeling 100%
  • Lyapunov Exponent 100%
  17 Citations (Scopus)

  314 Downloads (Pure)

• Resonance and Fractal Geometry

  Broer, H. W., Aug-2012, In: Acta applicandae mathematicae. 120, 1, p. 61-86 26 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Dynamical System 100%
  • Fractal Set 100%
  • Parameter Space 100%
  • Fractal Geometry 100%
  • Open Subset 100%
  14 Citations (Scopus)

  295 Downloads (Pure)
• 2011

  Dynamics and geometry near resonant bifurcations

  Broer, H., Holtman, S. J., Vegter, G. & Vitolo, R., Feb-2011, In: Regular & chaotic dynamics. 16, 1-2, p. 39-50 12 p.

  Research output: Contribution to journal › Article › Academic

  Open Access

  File

  • Dynamical System 100%
  • Equivariant 100%
  • Singularity Theory 100%
  • Vector Field 100%
  • Parameter Space 100%
  7 Citations (Scopus)

  348 Downloads (Pure)

• In Memoriam Floris Takens: A total mathematician

  Broer, H., 2011, In: Nieuw Srchief voor Wiskunde. 12, 1, p. 2024

  Research output: Contribution to journal › Article › Academic › peer-review

• Pacer cell response to periodic Zeitgebers

  Beersma, D. G. M., Broer, H. W., Efstathiou, K., Gargar, K. A. & Hoveijn, I., 15-Sept-2011, In: Physica D: Nonlinear Phenomena. 240, 19, p. 1516-1527 12 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Zeitgebers 100%
  • PACER 100%
  • Cell Response 100%
  • Circle Map 100%
  • Biological Rhythm 100%
  3 Citations (Scopus)

  356 Downloads (Pure)

• Quasi-periodic Bifurcations of Invariant Circles in Low-dimensional Dissipative Dynamical Systems

  Vitolo, R., Broer, H. & Simo, C., Feb-2011, In: Regular & chaotic dynamics. 16, 1-2, p. 154-184 31 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Invariant Circle 100%
  • Quasi-periodic Bifurcation 100%
  • Dissipative Dynamical Systems 100%
  • Circle 100%
  • Dynamical System 100%
  84 Citations (Scopus)

  484 Downloads (Pure)

• The dynamics of a low-order model for the Atlantic multidecadal oscillation

  Broer, H., Dijkstra, H., Simó, C., Sterk, A. & Vitolo, R., Jul-2011, In: Discrete and Continuous Dynamical Aystems. Series B. 16, 1, p. 73-107 35 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Strange Attractor 100%
  • Atlantic Multidecadal Oscillation 100%
  • Annuals 100%
  • Orbit 50%
  • Bifurcation 50%
  14 Citations (Scopus)
• 2010

  A geometric fractional monodromy theorem

  Lukina, O., Efstathiou, K. & Broer, H. W., 1-Aug-2010, In: Discrete and Continuous Dynamical Aystems. Series B. 3, 4, p. 517-532 16 p.

  Research output: Contribution to journal › Article › Academic › peer-review
  8 Citations (Scopus)

• Andrei N. Kolmogorov (1903-1987), bouwer van de kansaxioma's

  van den Brandhof, A., Broer, H. & Hart, K. P., 2010, In: Pythagoras. 49, 5, p. 18-23 6 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File
  109 Downloads (Pure)

• Chaos and quasi-periodicity in diffeomorphisms of the solid torus

  Broer, H. W., Simó, C. & Vitolo, R., Oct-2010, In: Discrete and Continuous Dynamical Aystems. Series B. 14, 3, p. 871-905 35 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  • Circle 100%
  • Diffeomorphism 100%
  • Strange Attractor 100%
  • Coincides 50%
  • Parametric 50%
  30 Citations (Scopus)

• Complexe getallen voor Wiskunde D en NLT

  Broer, H. & van der Straaten, K., 2010, In: Euclides. 85, 6, p. 239-241

  Research output: Contribution to journal › Article › Academic › peer-review

• Do Diophantine vectors form a Cantor bouquet?

  Broer, H., 2010, In: Journal of Difference Equations and Applications. 16, 5-6, p. 433-434 2 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Cantor Bouquet 100%
  • Vector Forms 100%
  • Diophantine 100%
  • Vector Form 100%
  3 Citations (Scopus)

  375 Downloads (Pure)

• Dynamical systems and chaos

  Broer, H. & Takens, F., 2010, Springer.

  Research output: Book/Report › Book › Academic

• Global qualitative analysis of a quartic ecological model

  Broer, H. & Gaiko, V. A., 15-Jan-2010, In: Nonlinear Analysis-Theory Methods & Applications. 72, 2, p. 628-634 7 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Limit Cycle 100%
  • Quartic 100%
  • Dynamical System 50%
  • Singular Point 50%
  • Global Bifurcation 50%
  13 Citations (Scopus)

  368 Downloads (Pure)

• Handbook of dynamical systems

  Broer, H., Takens, F. & Hasselblatt, B., 2010, Elsevier. 560 p.

  Research output: Book/Report › Book › Academic

• KAM Theory: Quasi-periodicity in Dynamical Systems

  Broer, H. W. & Sevryuk, M. B., 2010, Handbook of Dynamical Systems. Elsevier, p. 249-344 96 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

• New nonlinear mechanisms of midlatitude atmospheric low-frequency variability

  Sterk, A. E., Vitolo, R., Broer, H. W., Simo, C. & Dijkstra, H. A., 15-May-2010, In: Physica D: Nonlinear Phenomena. 239, 10, p. 702-718 17 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Low-frequency Variability 100%
  • Vorticity 100%
  • Midlatitudes 100%
  • Strange Attractor 100%
  • Atmospherics 100%
  20 Citations (Scopus)

  392 Downloads (Pure)

• Preliminaries of Dynamical Systems Theory

  Broer, H. W. & Takens, F., 2010, Handbook of Dynamical Systems. Elsevier, p. 1-42 42 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

  8 Citations (Scopus)

• Recognition of resonance type in periodically forced oscillators

  Broer, H. W., Holtman, S. J. & Vegter, G., 1-Sept-2010, In: Physica D: Nonlinear Phenomena. 239, 17, p. 1627-1636 10 p.

  Research output: Contribution to journal › Article › Academic › peer-review

  Open Access

  File

  • Poincaré Map 100%
  • Diffeomorphism 100%
  • Vector Field 100%
  • Parameter Space 100%
  • Lotka-Volterra System 100%
  3 Citations (Scopus)

  348 Downloads (Pure)