Non-linear stability of singular relative periodic orbits in Hamiltonian systems with symmetry

We generalize the sufficient condition for the stability of relative period ic orbits in symmetric Hamiltonian systems presented in [J. -P. Ortega, T.S . Ratiu, J. Geom. Phys. 32 (1999) 131-159] to the case in which these orbit s have non-trivial symmetry. We also describe a block diagonalization, simi lar in philosophy to the one presented in [J. -P. Ortega, T.S. Ratiu, Nonli nearity 12 (1999) 693-720] for relative equilibria, that facilitates the us e of this result in particular examples and shows the relation between the stability of the relative periodic orbit and the orbital stability of the a ssociated singular reduced periodic orbit. (C) 1999 Elsevier Science B.V. A ll rights reserved. Subj. Class.: Dynamical systems 1991 MSG: 34D35; 58F05.