2014/01/13 by Giuseppe Pucacco, Antonella Marchesiello · 1 citation
Physics and Astronomy · Mathematics · #nlin.CD #math-ph #math.MP
paper · pdf · doi:10.1016/j.physd.2013.12.009
published as PhysicaD 271 (2014) 10-18 · 22 pages, 3 figures, 1 table
arxiv created 2014/01/13 · arxiv updated 2014/01/14
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 \Z2×\Z2 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.