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arXiv · 1401.2855

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

Giuseppe Pucacco·Antonella Marchesiello
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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 $\Z_2\times\Z_2$ 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.

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Giuseppe Pucacco, Antonella Marchesiello. 2014-01-13. An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z_2 X Z_2 symmetry. https://doi.org/10.1016/j.physd.2013.12.009

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