0
2013
Impact Factor

# Juan Egea

Universidad de Murcia, 30100, Murcia, Spain
jeg@um.es
 Egea J., Ferrer S., van der Meer J. Hamiltonian Fourfold 1:1 Resonance with Two Rotational Symmetries 2007, vol. 12, no. 6, pp.  664-674 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 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 DOI:10.1134/S1560354707060081