Hamiltonian Fourfold 1:1 Resonance with Two Rotational Symmetries

    2007, Volume 12, Number 6, pp.  664-674

    Author(s): 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, Volume 12, Number 6, pp. 664-674

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