Symmetries in Hamiltonian systems are very common and play a fundamental role in the analysis of its bifurcation behavior. A solution that is invariant under the action of the symmetry is called a relative equilibrium. In this contribution we analyze by numerical continuation and a global symmetry reduction the existence of "bridges" between subharmonic bifurcations of relative equilibria. The constancy of the rotation number along the bridge is the key to extend the analysis to arbitrary tori.

This work has been done in collaboration with E. Freire, F. J. Mu\~noz Alamaraz, E. Doedel and A. Vanderbauwhede.