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 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.