An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z(2) x Z(2) symmetry

作者：Pucacco Giuseppe^*; Marchesiello Antonella

来源：Physica D: Nonlinear Phenomena , 2014, 271: 10-18.

DOI：10.1016/j.physd.2013.12.009

• Finite-dimensional Hamiltonian systems
• Perturbation theory
• Normal forms

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) x 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.

• 出版日期2014-3-15