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This article is cited in 8 scientific papers (total in 8 papers)
On the 65th birthday of R.Cushman
Hamiltonian Fourfold 1:1 Resonance with Two Rotational Symmetries
J. Egeaa, S. Ferrera, J.C. van der Meerb a Departamento de Matematica Aplicada, Facultad de Informatica,
Universidad de Murcia, 30100, Murcia, Spain
b Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven,
P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract:
In this communication we deal with the analysis of Hamiltonian Hopf bifurcations in 4-DOF systems defined by perturbed isotropic oscillators (1-1-1-1 resonance), in the presence of two quadratic symmetries $I_1$ and $I_2$. As a perturbation we consider a polynomial function with a parameter. After normalization, the truncated normal form gives rise to an integrable system which is analyzed using reduction to a one degree of freedom system. The Hamiltonian Hopf bifurcations are found using the 'geometric method' set up by one of the authors.
Keywords:
Hamiltonian system, bifurcation, normal form, reduction, Hamiltonian Hopf bifurcation, fourfold 1:1 resonance.
Received: 07.05.2007 Accepted: 05.10.2007
Citation:
J. Egea, S. Ferrer, J.C. van der Meer, “Hamiltonian Fourfold 1:1 Resonance with Two Rotational Symmetries”, Regul. Chaotic Dyn., 12:6 (2007), 664–674
Linking options:
https://www.mathnet.ru/eng/rcd646 https://www.mathnet.ru/eng/rcd/v12/i6/p664
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