Ferdinand Verhulst
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Ferdinand Verhulstmathematics Degrees
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Mathematics
Ferdinand Verhulst's Degrees
- PhD Mathematics Utrecht University
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(Suggest an Edit or Addition)Ferdinand Verhulst's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Averaging Methods in Nonlinear Dynamical Systems (1985) (1995)
- Nonlinear Differential Equations and Dynamical Systems (1989) (1333)
- Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics (2010) (225)
- Methods and applications of singular perturbations (2005) (219)
- Autoparametric Resonance in Mechanical Systems (2000) (190)
- Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella? (2009) (117)
- Singular perturbation methods for slow–fast dynamics (2007) (86)
- Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies (1979) (78)
- A Mechanism for Atmospheric Regime Behavior (2004) (59)
- Asymptotic Analysis II (1983) (51)
- Near-integrability of periodic FPU-chains (2000) (44)
- Symmetry and Resonance in Hamiltonian Systems (2001) (42)
- Averaging in vibration suppression by parametric stiffness excitation (2008) (41)
- Quenching of self-excited vibrations (2005) (40)
- The method of averaging (1990) (36)
- Suppressing Flow-Induced Vibrations by Parametric Excitation (2003) (36)
- Asymptotic Integrability and Periodic Solutions of a Hamiltonian System in $1:2:2$-Resonance (1984) (34)
- The Galerkin-averaging method for nonlinear, undamped continuous systems (1987) (33)
- Parametric and Autoparametric Resonance (1996) (33)
- Chaos in the 1:2:3 Hamiltonian normal form (1990) (33)
- Perturbation Analysis of Parametric Resonance (2009) (32)
- Parametric excitation in non-linear dynamics (2004) (29)
- Active and passive ocean regimes in a low-order climate model (2001) (25)
- Quasiperiodic phenomena in the Van der Pol-Mathieu equation (2009) (23)
- Symmetry and integrability in Hamiltonian normal forms (1997) (22)
- Henri Poincaré: Impatient Genius (2012) (22)
- Resonance in a rigid rotor with elastic support (1993) (21)
- Hamiltonian systems with widely separated frequencies (2003) (20)
- Periodic Solutions and Slow Manifolds (2007) (20)
- Two-body problem with slowly decreasing mass (1970) (20)
- Bifurcations of quasi-periodic dynamics: torus breakdown (2014) (19)
- Autoparametric resonance by coupling of linear and non-linear systems (1994) (18)
- Integrability and Non-integrability of Hamiltonian Normal Forms (2015) (18)
- Near-Integrability and Recurrence in FPU Chains with Alternating Masses (2018) (16)
- On averaging methods for partial differential equations (2007) (14)
- The Lyapunov exponents of the Van der Pol oscillator (2005) (14)
- Invariant Manifolds in Dissipative Dynamical Systems (2005) (13)
- Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass (1975) (13)
- Bifurcations of strongly non‐linear self‐excited oscillations (1994) (12)
- The dynamics of a low-order coupled ocean-atmosphere model (1998) (12)
- Autoparametric resonance of relaxation oscillations (2005) (12)
- On the number of isolating integrals in resonant systems with 3 degrees of freedom (1981) (11)
- The dynamics of slow manifolds (2007) (11)
- Vibration Problems ICOVP 2011 (2011) (11)
- Torus Bifurcations in a Mechanical System (2015) (11)
- Near-Integrability and Recurrence in FPU-Cells (2016) (10)
- Profits and Pitfalls of Timescales in Asymptotics (2015) (10)
- Averaging: the Periodic Case (2007) (10)
- The 1:2:4 resonance in a particle chain (2020) (10)
- The inhomogeneous Fermi-Pasta-Ulam chain (2015) (9)
- Approximations of higher order resonances with an application to Contopoulos' model problem (1979) (9)
- Asymptotic analysis of hamiltonian systems (1983) (9)
- Multiple solutions of a Generalized singular perturbed Bratu Problem (2012) (8)
- Asymptotic analysis from theory to application (1979) (8)
- A generalized Lane-Emden-Fowler equation (1982) (7)
- The hunt for canards in population dynamics: A predator–prey system (2014) (7)
- The Inhomogeneous Fermi-Pasta-Ulam Chain, a Case Study of the 1:2:3$1:2:3$ Resonance (2017) (7)
- Brouwer’s rotating vessel I: stabilization (2012) (6)
- On the Theory of Averaging (1976) (6)
- Averaging in non‐linear advective transport problems (1995) (6)
- Bifurcation of asymptotically stable periodic solutions in nearly impact oscillators (2009) (5)
- A chain of FPU cells (2015) (5)
- Dissipation-induced instabilities and symmetry (2011) (5)
- A Metaphor for Adiabatic Evolution to Symmetry (1995) (5)
- Psychoanalysis and chaos theory. (1999) (4)
- Henri Poincaré’s Inventions in Dynamical Systems and Topology (2016) (4)
- Dynamics of a Chain with Four Particles, Alternating Masses and Nearest-Neighbor Interaction (2018) (4)
- Two-body problem with decreasing mass: the autonomous case (1969) (4)
- The thermal stability of coronal loops by nonlinear diffusion asymptotics (1987) (4)
- Hamiltonian normal forms (2007) (4)
- Introduction to perturbation theory (1990) (4)
- The transition from elliptic to hyperbolic orbits in the two-body problem by slow loss of mass (1972) (4)
- Extension of Poincare's program for integrability, chaos and bifurcations (2012) (4)
- Recurrence and Resonance in the Cubic Klein-Gordon Equation (2019) (4)
- Stability analysis by the direct method (1990) (3)
- Mathematics is the art of giving the same name to different things : an interview with Henri Poincaré (2012) (3)
- Matched Asymptotic Expansions in the Two-body Problem with Quick Loss of Mass (1976) (3)
- Differential Equations and Dynamical Systems (2012) (3)
- The Two-Body Problem with a Decreasing Gravitational Constant (1976) (3)
- Emergence and Bifurcations of Lyapunov Manifolds in Nonlinear Wave Equations (2009) (3)
- Matched asymptotic expansions and singular perturbations: by Viktor Eckhaus. 145 pages, diagrams, tables, illustr., 612 × 912 in. Amsterdam, North Holland; New York, American Elsevier, 1973. Price, $8.95 (approx. £3·s50). (1975) (3)
- Variations on the Fermi-Pasta-Ulam Chain, a Survey (2020) (3)
- A note on higher order averaging (1988) (3)
- Some Elementary Exercises in Celestial Mechanics (2007) (2)
- Hunting French Ducks in Population Dynamics (2014) (2)
- Bifurcations of quasi-periodic dynamics: torus breakdown (2013) (2)
- Interaction of Lower and Higher Order Hamiltonian Resonances (2018) (2)
- Existence of stationary solutions in the coronal loop problem (1989) (2)
- Asymptotic analysis II : surveys and new trends (1983) (2)
- Recurrent canards producing relaxation oscillations. (2021) (2)
- Evolution to symmetry (2021) (1)
- Basic Material and Asymptotics (2007) (1)
- From A.Tondl's Dutch contacts to Neimark-Sacker-bifurcation (2022) (1)
- Evolution towards symmetry (1998) (1)
- Hype! An Exchange of Views (2014) (1)
- Authors' reply to “A remark to the paper by O. N. Kirillov and F. Verhulst “Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?” [Zamm 90, No. 6, 462–488 (2010)] (2012) (1)
- Nonlinear Diffusion in Stellar Magnetic Loops (1988) (1)
- Periodic solutions of continuous self-gravitating systems (1980) (1)
- Invariant manifolds and periodic solutions of three degrees of freedom Hamiltonian systems (1984) (1)
- High–low frequency interaction in alternating FPU α-chains (2021) (1)
- A Note on the Hénon-Heiles Problem (1976) (1)
- Linear Versus Nonlinear Stability in Hamiltonian Systems (2018) (1)
- Methodology of Averaging (2007) (1)
- The Theory of Averaging (1985) (1)
- The interaction of geometry and analysis in Henri Poincaré’s conceptions (2012) (1)
- Higher Order Resonance in Two Degree of Freedom Hamiltonian System (2001) (1)
- SPT 2004 - Symmetry and Perturbation Theory (2004) (1)
- Timescales and Error Estimates in Dynamical Systems (2013) (1)
- Near-Integrability and Recurrence in FPU Chains with Alternating Masses (2018) (1)
- Henri Poincaré: A Scientific Biography (2016) (1)
- Regular and chaotic recurrence in FPU cell-chains (2017) (1)
- The Inhomogeneous Fermi-Pasta-Ulam Chain , a Case Study of the 1 : 2 : 3 Resonance (2017) (1)
- Measures of Chaos in Hamiltonian Systems (2006) (1)
- Torus Break-down and Bifurcations in Coupled Oscillators☆ (2016) (1)
- Resonant periodic solutions in regularized impact oscillator (2021) (1)
- The validation of metaphors (1998) (0)
- Brouwer’s rotating vessel I: stabilization (2011) (0)
- At the End, What Kind of a Man? (2012) (0)
- Aspects of Poincaré’s Program for Dynamical Systems and Mathematical Physics (2012) (0)
- Evolution to Mirror-Symmetry in Rotating Systems (2021) (0)
- Aspects of Poincaré’s Program for Dynamical Systems and Mathematical Physics (2012) (0)
- Multiple solutions of a generalized one-dimensional Bratu problem (2011) (0)
- Historical Data and Biographical Details (2012) (0)
- Explorations for alternating FPU-chains with large mass (2020) (0)
- Recurrence and Resonance in the Cubic Klein-Gordon Equation (2019) (0)
- The Prize Competition of Oscar II (2012) (0)
- Classical (First-Level) Normal Form Theory (2007) (0)
- Periodic Averaging and Hyperbolicity (2007) (0)
- Book reviews (1976) (0)
- A Parametrically Excited Nonlinear Wave Equation (2020) (0)
- Poincaré’s Address to the Society for Moral Education (2012) (0)
- From Averaging to Normal Forms (2007) (0)
- Matched asymptotic expansions and singular perturbations : book review (1975) (0)
- The Inhomogeneous Fermi-Pasta-Ulam Chain, a Case Study of the 1:2:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1:2: (2017) (0)
- CHAPTER 3 Hamiltonian systems with Widely Separated Frequencies (2003) (0)
- Book ReviewEquations differentielles et fonctionnelles non lineaires: Edited by P. Janssens, J. Mawhin and N. Rouche. 624 pages, diagrams, figures, 612 x 912 in., Hermann, Paris, 1974. Price, $28.00 (approx). (1978) (0)
- Book-Review - Asymptotic Analysis from Theory to Application (1980) (0)
- Integrability and Non-integrability of Hamiltonian Normal Forms (2014) (0)
- The dynamics of internal and inertial waves in enclosed basins (1998) (0)
- Instabilities induced by dissipation (2009) (0)
- Viewpoint Hype ! An Exchange of Views (2014) (0)
- Introduction to the paper by V.F. Butuzov and A.B. Vasil’eva (1983) (0)
- Philosophy and Essays (2012) (0)
- Averaging in damping by parametric stiffness excitation (2007) (0)
- and Vincent Rivasseau ( eds . ) : Henri Poincaré , 1912 – 2012 A global view of Poincaré ’ s scientific work (2017) (0)
- Higher-Level Normal Form Theory (2007) (0)
- Introduction to the theory of stability (1990) (0)
- Averaging normal forms for PDEs with applications to perturbed wave equations (2008) (0)
- Averaging over Angles (2007) (0)
- Time-reversal, tori families,\query{Q1} and canards in the Sprott A and NE9 systems. (2022) (0)
- SENSITIVITY ANALYSIS OF DISSIPATIVE REVERSIBLE AND HAMILTONIAN SYSTEMS: A SURVEY (2009) (0)
- The dynamics of Hamiltonians with non-integrable normal form (2015) (0)
- Mitropolsky, Yu. A.; Lopatin, A. K.: Nonlinear Mechanics, Groups and Symmetry. Dordrecht etc., Kluwer Academic Publishers 1995. IX, 377 pp., Dfl. 255.–. ISBN 0-7923-3339-X (Mathematics and Its Applications 319) (1997) (0)
- Hype! An Exchange of Views (2014) (0)
- Asymptotic wave theory: M. Roseau, 349 pp., diagrams, tables, 612× 912× in., American Elsevier New York, North-Holland Series in Applied Mathematics and Mechanics, Vol. 20, 1976, Price $46.25. (1977) (0)
- The History of the Theory of Averaging (2007) (0)
- Bifurcation of asymptotically stable periodic solutions inearly impact oscillators : DRAFT (2021) (0)
- Recurrence and diffusion in FPU chains with alternating masses (2017) (0)
- Henri poincare impatient genius / Ferdinand Verhulst (2012) (0)
- Emergence of Slow Manifolds in Nonlinear Wave Equations (2007) (0)
- Book Review: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Proceedings of the IUTAM Symposium held in Ithaca, NY, USA, 27 July–1 August 1997. by Francis C. Moon (ed.) (2004) (0)
- Resonances in dynamical systems with discrete symmetry - The Henon-Heiles problem (1979) (0)
- Quenching Damping-Induced Instability (2011) (0)
- The Poincaré-Lindstedt method (1996) (0)
- The description of jumps between Kepler orbits by boundary layer methods (1979) (0)
- Asymptotics of Slow-time Processes, First Steps (1985) (0)
- Nilpotent (Classical) Normal Form (2007) (0)
- Multiple timing and spatial scaling for bifurcations (2023) (0)
- Introduction to the research papers (1983) (0)
- Introduction to the paper by A.S. Bakaj (1983) (0)
- Invariant Manifolds by Averaging (2007) (0)
- Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations (2010) (0)
- On averaging methods for partial di erential equations preprint (2006) (0)
- Stability by linearisation (1990) (0)
- Academic Education: 1873–1879 (2012) (0)
- From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory (2019) (0)
- Equations differentielles et fonctionnelles non lineaires (1978) (0)
- Comment on the paper by Kirkinis on the renormalization method (2012) (0)
- Bifurcations and instability phenomena in parametric dynamics (2013) (0)
- BIFURCATIONS IN FLOW-INDUCED VIBRATION (2003) (0)
- Book Review: Partial Differential Equations in Mechanics. By A. P. C. Selvadurai (2002) (0)
- Averaging Over Angles with an Application to Rotor Dynamics (1987) (0)
- Henri Poincaré's neglected ideas (2020) (0)
- Henri Poincaré (1854–1912) Engineer, Mathematician, Physicist and Philosopher (2018) (0)
- Career in Paris (2012) (0)
- Torus Bifurcations in a Mechanical System (2013) (0)
- A special issue for Henri Poincaré (2012) (0)
- An Asymptotic-Numerical Approach to the Coronal Loop Problem (1990) (0)
- A 4-Dimensional Example of Hopf Bifurcation (2007) (0)
- Hamiltonian Normal Form Theory (2007) (0)
- Non-linear Ordinary Differential Equations and Dynamical Systems, Introduction to (2009) (0)
- Impressive Results in Vesoul and Caen (2012) (0)
- Optical-acoustical interaction in FPU-chains with alternating large masses (plus appendix) (2020) (0)
- ACTIVE AND DEGENERATE RESONANCES IN CHAINS OF OSCILLATORS (2009) (0)
- Hamiltonian and dissipative passage through resonance (2018) (0)
- New books about Henri Poincaré (2012) (0)
- Approximation of Integrals (2005) (0)
- Averaging: the General Case (2007) (0)
- Systems with fast limit cycles and slow interaction (2019) (0)
- Averaging over Spatial Variables: Systems with Slowly Varying Frequency and Passage through Resonance (1985) (0)
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