On relative normal modes

We generalize the Weinstein-Moser theorem on the existence of nonlinear nor mal modes near an equilibrium in a Hamiltonian system to a theorem on the e xistence of relative periodic orbits near a relative equilibrium in a Hamil tonian system with continuous symmetries. In particular, we prove that unde r appropriate hypotheses there exist relative periodic orbits near relative equilibria even when these relative equilibria are singular points of the corresponding moment map, i.e. when the reduced spaces are singular. (C) Ac ademie des Sciences/Elsevier, Paris.