Splitting equivariant dynamics

Giuseppe Gaeta Centre de Physique Th eorique, Ecole Polytechnique F 91128 Palaiseau (France) and Departamento de Fisica Teorica II, Universidad Complutense E 28040 Madrid (Spain) Summary. We prove that any dynamical system on a G-manifold M which is equivariant under the G action, can be decomposed into the semidirect product of an autonomous dynamics in the G-orbit space = M=G, and a dynamics (depending on the G-orbit) on G. This result is actually a corollary of Michel theorem [1] on the geometry of symmetry breaking, and uses the same ingredients for the proof. It permits to unify a number of known and useful results in the literature, as discussed here.