Jan Cees van der Meer

P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven


Egea J., Ferrer S., van der Meer J.
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
Citation: Egea J., Ferrer S., van der Meer J.,  Hamiltonian Fourfold 1:1 Resonance with Two Rotational Symmetries, Regular and Chaotic Dynamics, 2007, vol. 12, no. 6, pp. 664-674

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