An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z_2 X Z_2 symmetry

Abstract

We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. The rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods. The geometric approach readily allows to find an energy-momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features. Quadrature formulas for the actions, periods and rotation number are also provided.

22 pages, 3 figures, 1 table

References in corpus (1)

• Equivariant singularity analysis of the 2:2 resonance

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