Universidad de Murcia, 30100, Murcia, Spain
Departamento de Matematica Aplicada, Facultad de Informatica
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
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.