We present a general review of the bifurcation sequences of periodic orbits
in general position of a family of resonant Hamiltonian normal forms with
nearly equal unperturbed frequencies, invariant under Z2×Z2
symmetry. The rich structure of these classical systems is investigated with
geometric methods and the relation with the singularity theory approach is also
highlighted. The geometric approach is the most straightforward way to obtain a
general picture of the phase-space dynamics of the family as is defined by a
complete subset in the space of control parameters complying with the symmetry
constraint. It is shown how to find an energy-momentum map describing the phase
space structure of each member of the family, a catastrophe map that captures
its global features and formal expressions for action-angle variables. Several
examples, mainly taken from astrodynamics, are used as applications.Comment: 36 pages, 10 figures, accepted on International Journal of
Bifurcation and Chaos. arXiv admin note: substantial text overlap with
arXiv:1401.285
