Equivariant singularity analysis of the 2:2 resonance

Abstract

We present a general analysis of the bifurcation sequences of 2:2 resonant reversible Hamiltonian systems invariant under spatial ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. The rich structure of these systems is investigated by a singularity theory approach based on the construction of a universal deformation of the detuned Birkhoff normal form. The thresholds for the bifurcations are computed as asymptotic series also in terms of physical quantities for the original system.

28 pages, 2 figures

References in corpus (1)

• On the Orbit Structure of the Logarithmic Potential

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