A selection of papers before 1993
- 1970, Verhulst, F. and Eckhaus, W. - Two-body problem with slowly decreasing mass,
Int. J. Nonlinear Mech. 5, pp. 617-624.
- 1975, Verhulst, F. - Asymptotic expansions in the perturbed two-body problem with application to systems with
variable mass, Celes. Mech. 11, pp. 95-129.
- 1976, Verhulst, F. - Matched asymptotic expansions in the two-body problem with quick loss of mass,
J. Inst. Math. Applics. 18, pp. 87-98.
- 1976, Hut, P. and Verhulst, F. - The two-body problem with a decreasing gravitational constant,
Mon. Not. Roy. Astr. Soc. 177, pp. 545-549.
- 1979, Verhulst, F. - Discrete-symmetric dynamical systems at the main resonances with applications to axi-symmetric
galaxies, Phil. Trans. roy. Soc. London A 290, pp. 435-465.
- 1979, Sanders, J.A. and Verhulst, F. -Approximation of higher-order resonances with an application to Contopoulos' model problem, in
``Asymptotic Analysis,
from theory to application'', Lecture Notes in Math. 711 (F. Verhulst ed.), Springer-Verlag pp. 209-228.
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- 1981, Martinet, L., Magnenat,P. and Verhulst, F. - On the number of isolating integrals in resonant systems
with three degrees of freedom, Celes. Mech. 29, pp. 93-99.
- 1984, Van der Aa, E. and Verhulst, F. - Asymptotic integrability and periodic solutions of a Hamiltonian
system in 1:2:2-resonance, SIAM J. Appl. Math. Analysis 15, pp. 890-911.
- 1987, Stroucken, A.C.J. and Verhulst, F. - The Galerkin-averaging method for nonlinear, undamped continuous
systems, Math. Meth. Appl. Sciences 9, pp. 520-549.
- 1987, Van den Broek, B. and Verhulst, F. - Averaging techniques and the oscillator-flywheel problem,
Nieuw Archief v. Wiskunde 4th series, vol. 5, pp. 185-206, pdf file
- 1988, Verhulst, F. - A note on higher-order averaging, Int. J. Nonlinear Mech. 23, pp. 341-346.
- 1990, Hoveijn, I. and Verhulst, F. - Chaos in the 1:2:3- Hamiltonian normal form, Physica D, 44, pp. 397-406.
- 1991, Verhulst, F. and Hoveijn, I. - Integrability and chaos in Hamiltonian normal forms, in ``Geometry and
Analysis'' (H.W. Broer and F. Takens, eds.), Pitman Res. Notes in Math.
Papers 1993--2014
- 1993, Verhulst, F. - Bifurcations and chaotic phenomena in mechanical
systems, Proc. 1st European Nonlinear Oscillations Conference (E.
Kreuzer and G. Schmidt, eds.), Mathematical Research vol. 72,
Akademie Verlag, Berlin 1993.
- 1993, Ruijgrok, M., Tondl, A., Verhulst, F. - Resonance in a rigid rotor with elastic support, Z. angew. Math. Mech. 73, 10, 255-263.
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Note that the question raised in section 4 is answered by I.Hoveijn and MRuijgrok in Z. Angew. Math. Phys. 46, pp. 384-392 (1995).
- 1994, Svoboda, R, Tondl, A., Verhulst, F. - Autoparametric resonance by coupling of linear and nonlinear systems, Int. J. Non-linear
Mechanics 29, 2, pp. 225-232. pdf file
- 1994, Doelman, A., Verhulst, F. - Bifurcations of strongly nonlinear self-
excited oscillations, Mathematical Methods in the Applied Sciences
17, pp. 189-207.
- 1994, Verhulst, F. - Metaphors for psychoanalysis, Monlinear Science Today 4, pp. 1-6.
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- 1995, Heijnekamp, J.J., Krol, M.S., Verhulst, F. - Averaging in nonlinear advective transport problems, Mathematical Methods in the
Applied Sciences 18. pp. 437-448.
- 1996, Ruigrok, M. en Verhulst, F.- Parametric and autoparametric resonance, in Nonlinear Dynamical Systems and Chaos (eds. H.W.Broer, S.A. van Gils, I.Hoveijn, F.Takens), pp. 279-298, Birkh\"auser, Basel
- 1996, F.Verhulst - Autoparametric resonance, survey and new results, Proc. 2nd European Nonlinear Oscillations Conference
(eds. Pust,H, Peterka, F.), Euromech vol. 1, pp. 483-488, Prague.
- 1997, R.J.A.G.Huveneers and F.Verhulst - A metaphor for adiabatic evolution to symmetry,
SIAM J. Appl. Math. 57, pp. 1421-1442.
- 1998, F. Verhulst - Symmetry and integrability in Hamiltonian normal forms, in ``Symmetry and Perturbation Theory'' (D. Bambusi and G. Gaeta, eds.), Quaderni GNFM, Firenze 1998.
- 1998, F. Verhulst and R.J.A.G. Huveneers - Evolution towards Symmetry, Regular and Chaotic Dynamics V.3, pp. 45-55 (1998), Moscow.
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- 1999, Ferdinand Verhulst - On averaging methods for partial differential equations, in ``Symmetry and Perturbation Theory, SPT 98'' pp. 79-95, (A. Degasperis and G. Gaeta, eds.), World Scientific, Singapore etc.
- 2000, Bob Rink and Ferdinand Verhulst - Near-integrability of periodic FPU-chains,
Physica A 285, pp. 467-482.
- 2000, J.M. Tuwankotta and F. Verhulst - Symmetry and Resonance in Hamiltonian Systems, SIAM Journal on Applied Mathematics 61, pp. 1369-1385.
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- 2001, J.M. Tuwankotta and F. Verhulst - Higher order resonance in two degree of freedom Hamiltonian system, in ''Symmetry and Perturbation Theory'', Proc. Intern. Conf. SPT2001 (D. Bambusi, G. Gaeta, M. Cadoni, eds.) pp. 206-213, World Scientific, Singapore (ISBN 981-02-4793-1).
- 2001, Lennaert van Veen, Theo Opsteegh and Ferdinand Verhulst -
Active and passive ocean regimes in a low-order climate model,
Tellus vol. 53A, pp. 616-528.
- 2002, Ferdinand Verhulst - Parametric and Autoparametric Resonance,
Acta Applicandae Mathematicae 70, pp. 231-264.
- 2002, S. Fatimah and F. Verhulst - Bifurcation in Flow-induced Vibration, in ``Symmetry and Perturbation Theory'', SPT2002 (proc. of the conference
held in Cala Gonone, 19-26 May 2002), S. Abenda, G. Gaeta, S. Walcher, eds., pp. 51-55, World Scientific, Singapore (ISBN 981-238-241-0).
- 2003, S. Fatimah and F. Verhulst -
Suppressing flow-induced vibrations by parametric excitation,
Nonlinear Dynamics 23, pp.275-297.
- 2003, J.M. Tuwankotta and F. Verhulst -
Hamiltonian Systems with Widely Separated Frequencies,
Nonlinearity 16, pp. 689-706.
- 2004, T. Bakri, R. Nabergoj, A. Tondl and F. Verhulst -
Parametric excitation in nonlinear dynamics, International Journal of Non-Linear Mechanics,
vol 39/2 pp 311 - 329, pdf file
- 2004, D. Crommelin, J.D. Opsteegh and F. Verhulst -
Atmospheric regime behaviour, Journal of the Atmospheric Sciences,
vol 61, pp 1406 - 1419, pdf file
- 2005, Johan Grasman, Ferdinand Verhulst and Shagi-Di Shih -
The Lyapunov exponents of the Van der Pol oscillator,
Mathematical Methods in the Applied Sciences pdf file
28, pp. 1131-1139.
- 2005, F. Verhulst and Abadi - Autoparametric Resonance of Relaxation Oscillations, ZAMM 85, pp. 122-131.
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- 2005, Ferdinand Verhulst -
Invariant manifolds in dissipative dynamical systems, Acta Applicandae Mathematicae 87, pp. 229-244.
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- 2005, Ferdinand Verhulst -
Quenching of self-excited vibrations, J. Engineering Math. 53, pp. 349-358.
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- 2006, Ferdinand Verhulst -
Measures of Chaos in Hamiltonian Systems, Proc. 2d Int. Conf. Nonlinear Normal
Modes and Localization in Vibrating Systems, Samos, June 19-23, 2006.
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- 2007, Ferdinand Verhulst and Taoufik Bakri -
The dynamics of slow manifolds, J. Indones. Math. Soc., vol. 13, pp. 73-90.
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- 2007, Ferdinand Verhulst -
Periodic solutions and slow manifolds, Int. J. Bifurcation
and Chaos, vol. 17, no. 8. pp. 2533-2540.
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- 2007, Ferdinand Verhulst -
Hamiltonian normal forms:
Scholarpedia
- 2007, Ferdinand Verhulst -
Emergence of slow manifolds in nonlinear wave equations, SPT2007 (proc. of the conference
held in Otranto, Italy, June 2007),World Scientific (Gaeta, Vitolo and Walcher, eds.) pp. 206-214.
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- 2008, Fadi Dohnal and Ferdinand Verhulst -
Averaging in damping by parametric stiffness excitation, Nonlinear Dynamics 54,
pp. 231-248.
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- 2009, Taoufik Bakri, Hil G.E. Meijer and Ferdinand Verhulst -
Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations,
Journal of Nonlinear Science 19, pp. 1432-1467.
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- 2009, Ferdinand Verhulst -
Perturbation analysis of parametric resonance, Encyclopedia of Complexity and Systems Science,
Springer.
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- 2009, F. Veerman and F. Verhulst -
Quasiperiodic phenomena in the Van der Pol-Mathieu equation, J. of Sound and Vibration.326, pp. 314-320.
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- 2009, Ferdinand Verhulst en Oleg Kirillov -
Bottema opende Whitney's paraplu (in Dutch), Nieuw Archief voor Wiskunde,
5e serie, deel 10, pp. 250-254.
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- 2010, Oleg Kirillov and Ferdinand Verhulst -
Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?,
ZAMM 90, pp. 462-488.
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- 2010, Ferdinand Verhulst -
Averaging Normal Forms for PDEs with applications to perturbed wave equations,
in Integral Methods in Science and Engineering, Analytic Methods, C. Constanda
and M.E. Perez, eds., vol. I, pp. 307-321, Birkhauser.
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- 2010, Ferdinand Verhulst -
Eine kuhle Sicht der Wahrheit, in Das Zebra-Buch zur Geometrie, F. Verhulst
and S. Walcher, eds., pp. 199-247, Springer.
- 2011, Jiri Naprstek, Jaromir Horacek, Miloshav Okrouhlik, Bohdana Marvalova,
Ferdinand Verhulst, Jerzy T. Sawicki, eds. -
Vibration Problems, ICOVP 2011,
Springer Proceedings in Physics 139, The 10th International Conference on Vibration Problems,
Springer.
- 2011, Ferdinand Verhulst -
Quenching Damping-Induced Instability, in
Jiri Naprstek, Jaromir Horacek, Miloshav Okrouhlik, Bohdana Marvalova,
Ferdinand Verhulst, Jerzy T. Sawicki, eds. -
Vibration Problems, ICOVP 2011,
Springer Proceedings in Physics 139, The 10th International Conference on Vibration Problems,
Springer, pp. 543-547.
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- 2011, Ferdinand Verhulst, section editor -
Non-Linear Ordinary Differential Equations and Dynamical Systems,
Mathematics of Complexity, 3 vols., 1858 pp. Robert A. Meyers, ed.-in-chief,
Springer.
- 2011, Ferdinand Verhulst -
Perturbation Analysis of Parametric Resonance,
in Mathematics of Complexity, vol. 3., Robert A. Meyers, ed.-in-chief,
pp. 1251-1264, Springer.
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- 2011, Ferdinand Verhulst -
Brouwer's rotating vessel I: stabilization,
ZAMP, published online December 2011, DOI 10.1007/s00033-011-0177-5.
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- 2011, Ferdinand Verhulst -
Extension of Poincare's program for integrability, chaos and bifurcations,
Chaotic Modeling and Simulation, October 2011 pp. 3-16.
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- 2012, Ferdinand Verhulst -
Aspects of Poincare's program for dynamical systems and mathematical physics,
Acta Applicandae Mathematicae, 120, pp. 299-315.
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- . 2012, Taoufik Bakri, Yuri. A. Kuznetsov, Ferdinand Verhulst, Eusebius Doedel -
Multiple solutions of a generalized singularly perturbed Bratu problem,
International Journal of Bifurcation and Chaos 22, no. 4 (1250095).
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- . 2012, Ferdinand Verhulst and Steven Wepster, eds.-
Henri Poincare Centennial Issue,
Nieuw Archief voor Wiskunde 13 (3), September 2012.
- . 2012, Ferdinand Verhulst -
The interaction of geometry and analysis in Henri Poincare's conceptions,
Henri Poincare Centennial Issue,
Nieuw Archief voor Wiskunde 13 (3), September 2012, pp. 209-216.
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- . 2012, Ferdinand Verhulst -
Mathematics is the art of giving the same name to different things, an interview with Henri Poincare,
Henri Poincare Centennial Issue,
Nieuw Archief voor Wiskunde 13 (3), September 2012, pp. 154-158.
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- . 2012, Jean-Marc Ginoux, Ferdinand Verhulst, Jeremy Gray -
New books about Henri Poincare,
Henri Poincare Centennial Issue,
Nieuw Archief voor Wiskunde 13 (3), September 2012, pp. 220-222.
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- . 2012, Ferdinand Verhulst, -
Henri Poincare, impatient genius
Scientific biography, Springer, New York, 260 pp. ISBN 978-1-4614-2406-2
- . 2013, Taoufik Bakri and Ferdinand Verhulst -
Bifurcations of quasi-periodic dynamics: torus breakdown,ZAMP DOI 10.1007/s000033-013-0363-8.
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- . 2013, Taoufik Bakri, Yuri. A. Kuznetsov, Ferdinand Verhulst -
Torus bifurcations in a mechanical system,
Journal of Dynamics and Differential Equations, DOI 10.1007/s10884-013-9339-9.
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- . 2013, Ferdinand Verhulst -
Henri Poincar\'e en het ontstaan van de topologie, (in Dutch)
Vakantiecursus voor leraren, CWI en TUE,pp. 59-79, augustus 2013.
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- . 2013, Ferdinand Verhulst -
Timescales and error estimates in dynamical systems,
Chaotic Modeling and Simulations (CMSIM) 4, pp. 473-494 (CHAOS conference, Istanbul June
2013).
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- . 2014, Ferdinand Verhulst -
Proc. in Mathematics and Statistics,
Proc. in Mathematics and Statistics: Applied Non-Linear Dynamical Systems/DSTA 2013
(Jan Awrejcewicz, ed.) pp. 319-335, Springer 2014.
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- . 2014, Ferdinand Verhulst -
Bifurcations and instability phenomena in parametric dynamics,
Euromech 532, 1st International Colloquium on Time-periodic Systems, August 27-30, 2012.
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- . 2014, Ferdinand Verhulst, Steven Krantz and Neal Koblitz -
Hype! An exchange of views,
The Mathematical Intelligencer 36 (3), pp. 8-13.
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- . 2014, Ferdinand Verhulst -
The hunt for canards in population dynamics: A predator-prey system,
International Journal of Non-Linear Mechanics 67, pp. 371-377.
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- . 2014, Ferdinand Verhulst -
How to analyse Hamiltonian non-integrability,
Canadian Mathematical Society Notes 46 (6) pp. 12-13.
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- . 2015, Ferdinand Verhulst -
Integrability and non-integrability of Hamiltonian normal forms,
Acta Applicandae Mathematicae 137 pp. 253-272, DOI 10.1007/s10440-014-9998-5.
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- . 2015, Ferdinand Verhulst -
Profits and pitfalls of timescales in asymptotics,
SIAM Review 57, pp. 255-274.
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- . 2015, Ferdinand Verhulst -
A chain of FPU cells, 13th International Conference Dynamical Systems - Theory and Applications,
Proc. vol. Control and Stability (eds. J.Awrejcewicz, M.Kazmierczak, J.Mrozowski, P.Oleinik)
pp. 603-612, Lodz, December 7-10, 2015.
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- . 2016, Ferdinand Verhulst -
Book Review: Henri Poincare: a scientific biography, by Jeremy Gray,
The European Legacy, towards new paradigms 2016, Routledge, Taylor and Francis Group,
DOI: 10.1080/10848770.2016.1150077
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- . 2016, Ferdinand Verhulst -
Torus break-down and bifurcations of coupled oscillators;
Procedia IUTAM 19, pp. 5-10 (also avaliable at www.sciencedirect.com),
DOI: 10.1016/j.piutam.2016.03.003
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- . 2016, Ferdinand Verhulst -
Henri Poincare's inventions in dynamical systems and topology,
Ch. 1 in "The foundations of chaos revisited: from Poincare to recent advancements", (Christos Skiadas, ed.),
pp. 1-25, Springer, 2016
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- . 2016, Ferdinand Verhulst -
Regular and chaotic recurrence in FPU-cells,
Applied Mathematical Modelling 46, pp. 763-770 (printed 2017) = dx.doi.org./10.1016/j.apm.2016.06.047
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- . 2016, Ferdinand Verhulst -
Near-integrability and recurrence in FPU cell-chains,
Int. J. Bifurcation and Chaos 26, no. 14 (23 pp.)
DOI: 10.1142/S0218127416502308
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- . 2016, Ferdinand Verhulst -
Vergeet `zuivere en toegepaste' wiskunde',
Nieuw Archief voor Wiskunde 17, pp. 295-297.
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- . 2017, Ferdinand Verhulst -
Book Review: A global view of Poincar's scientific work, Duplantier and Rivasseau eds.
Nieuw Archief voor Wiskunde 18, pp. 69-71.
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- . 2017, Roelof Bruggeman and Ferdinand Verhulst -
The inhomogeneous Fermi-Pasta-Ulam chain, a case study of the 1:2:3 resonance,
Acta Appl Math 28 June 2017 DOI 10.1007/s10440-017-0115-4.
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- . 2017, Ferdinand Verhulst -
Linear versus nonlinear stability in Hamiltonian systems,
Recent trends in Applied Nonlinear Mechanics and Physics, Proc. in Physics 199 (M. Belhaq, ed.) pp. 121-128, (2018)
Springer, DOI 10.1007/978-3-319-63937-6-6.
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- . 2017, Ferdinand Verhulst -
Dynamics of a chain with four particles, altenating masses and nearest-neighbour interaction,
Recent trends in Applied Nonlinear Mechanics and Physics, Proc. in Physics 199 (M. Belhaq, ed.) pp. 103-120 (2018),
Springer, DOI 10.1007/978-3-319-63937-6-6,
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- . 2017, Ferdinand Verhulst -
Hamiltonian and dissipative passage through resonance,
Chaotic Modeling and Simulations (CMSIM) 4, pp. 419-432 (CHAOS conference, Barcelona,
June 2017).
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- . 2017, Ferdinand Verhulst -
Recurrence and diffusion in FPU chains with alternating masses,
Chaotic Modeling and Simulations (CMSIM) 4, pp. 543-446 (CHAOS conference, Barcelona,
June 2017).
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- 2018, Roelof Bruggeman and Ferdinand Verhulst -
Near-integrability and recurrence in FPU chains with alternating masses,
J. Nonlinear Science, Springer
DOI 10.1007/s00332-018-9482-x
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- 2018, Ferdinand Verhulst -
Interaction of lower and higher order Hamiltonian resonances,
International Journal of Bifurcation and Chaos 28, no. 8,
(doi:10.1142/S0218127418500979).
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- 2019, Ferdinand Verhulst -
Recurrence and Resonance in the Cubic Klein-Gordon Equation
Acta Appl Math, 162, pp. 145-164 (2019) DOI: 10.1007/s10440-019-00238-4
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- 2019, Ferdinand Verhulst -
Henri Poincare's neglected ideas,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 2019 (eds T. Hagen, A. Johann, H.-P. Kruse, F. Rupp, S. Walcher)
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- 2019, Ferdinand Verhulst -
Inleiding op leven en werk van Laplace, 8 pp. in Dutch,
in ''Zo is het, De bewijzen van Laplace'' auteur Cees Andriesse, Epsilon Uitgaven 2019,
ISBN 978 9050 4117 90,
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- 2019, Ferdinand Verhulst - Systems with fast limit cycles and slow interaction,
Proc. Conference: DYNAMICAL SYSTEMS -- THEORY AND APPLICATIONS T2, Applicable solutions in non-linear dynamical systems pp. 511-522
(Jan Awrejcewicz, Marek Ka\'zmierczak, Pawel Olejnik, eds.) Lodz, Poland, Dec. 2019.
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- 2020, Ferdinand Verhulst and Johan M. Tuwankotta - A parametrically excited
nonlinear wave equation, A.K. Abramian eo al. (eds.), Nonlinear Dynamics of
Discrete and Continuous Systems, Advanced Strucural Materials vol. 139,
doi.org/10.1007/978-3-030-53006-8_11
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- 2021, Ferdinand Verhulst - High-low frequency interaction in alternating
FPU alfa-chains, Int. J. Non-Linear Mechanics.
ISSN 0020-7462, https://doi.org/10.1016/j.ijnonlinmec.2021.103686.
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- 2021, Ferdinand Verhulst - Evolution to mirror-symmetry in rotating
systems, Symmetry (MDPI Journal) special issue Slow-fast dynamical systems,
1 July 2021, 13; doi.org/10.3390/sym13071189, also arXiv 2111.01569;
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- 2021, Heinz Hanssmann, Reza Mazrooei-Sebdani and Ferdinand Verhulst, - The 1:2:4 resonance in a particle chain, Indagationes Mathematicae
doi.org/10.1007/978-??
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- 2021, Ferdinand Verhulst - Variations on the FPU-chain, a survey,
13th Chaotic Modelling and Simulation Conference (2020), C. Skiadas (ed.)
ch. 71 (springer)
doi.org/10.1007/978 ??
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- 2021, Oleg Makarenkov and Ferdinand Verhulst - Resonant periodic solutions
in regularized impact oscillator,
J.Math.An.Applications vol. 499, 2,
doi:10.1016/j.jmaa.2021.125035
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- 2021, Wilberd van der Kallen and Ferdinand Verhulst - Explorations for
alternating FPU-chains with large mass,
Int. J. Non-Linear Mech. vol. 137,103809 (free access)
doi:10.1016/j.jmaa.2021.125035
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- 2022, Oleg N. Kirillov and Ferdinand Verhulst - From rotating fluid masses
and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory,
in ``Mathematics inspired by Applications'', (M. Guenther and W. Schilders eds.)
Springer.
- 2022, Ferdinand Verhulst - Perturbation Theory of Parametric Resonance,
in Perturbation Theory, vol. in Encycloperia of Complexity and Systems Science Series (Giuseppe Gaeta ed. )
pp. 167-183, Springer.
- 2022, Taoufik Bakri and Ferdinand Verhulst - From A.Tondl's Dutch contacts
to Neimark-Sacker bifurcation,
in Applied and Computational Mechanics (ACM) vol. 16, pp. 87-100
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- 2023, Ferdinand Verhulst - De uitvinding van de relativiteitstheorie
(in Dutch),
in `Nieuw Archief voor Wiskunde (NAW),5e serie, deel 24-1 pp. 55-56.
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- 2023, Ferdinand Verhulst - Multiple Timimg and Spatial Scaling for
Bifurcations, Feature Paper
in Nonlinear Dynamics 111,pp. 10693-10707.
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- 2023, Ferdinand Verhulst - A Toolbox of Averaging Theorems, ordinary and partial differential equations,
Surveys and Tutorials in the Applied Mathematical Sciences 12
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- 2023, Ferdinand Verhulst - Evolution to mirror-symmetric galaxies,
preprint http://arxiv.org/abs/2310.11916
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- 2024, Taoufik Bakri and Ferdinand Verhulst - Emergence and Approximation of Tori, in CSNDD Int. Conf. on Structural Nonlienar Dynamics and Diagnosis
(M. Belhaq ed.), Marrakech May 1517, 2023.
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- 2024, Ferdinand Verhulst - Een mathematisch fysicus over Dennett en Metzinger; review of books on consciousness and evolution, text Dutch with English summary.
preprint http://arxiv.org/abs/2310.11916
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- 2024, Ferdinand Verhulst and Taoufik Bakri - Nonintegrability of 3 D0F Hamiltonian Resonant Systems; International J. Bifurcation \& Chaos,34, no. 13
DOI: 10.1142/S0218127421501682
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- 2024, Ferdinand Verhulst and Taoufik Bakri - The Sprott B system;
Chaos, 1, 34: 103116;
DOI: 10.1063/5.0212565
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