Hamiltonian fourfold 1:1 resonance with two rotational symmetries

J. Egea, S. Ferrer, J.C. Meer, van der

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)664-674
JournalRegular and Chaotic Dynamics
Issue number6
Publication statusPublished - 2007


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