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.
Pucacco, G., Marchesiello, A. (2014). An energy-momentum map for the time-reversal symmetric 1:1 resonance with $\Z_2\times\Z_2$ symmetry. PHYSICA D-NONLINEAR PHENOMENA, 271, 10-18 [doi:10.1016/j.physd.2013.12.009].
An energy-momentum map for the time-reversal symmetric 1:1 resonance with $\Z_2\times\Z_2$ symmetry
PUCACCO, GIUSEPPE;
2014-01-01
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.File | Dimensione | Formato | |
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