Hamiltonian fourfold 1:1 resonance with two rotational symmetries |
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Authors: | J. Egea S. Ferrer J. C. van der Meer |
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Affiliation: | (1) Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Murcia, Spain;(2) Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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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. |
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Keywords: | Hamiltonian system bifurcation normal form reduction Hamiltonian Hopf bifurcation fourfold 1:1 resonance |
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