G. Gaeta
Splitting equivariant dynamics
(39K, TeX)

ABSTRACT.  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
$\Om = M / G$, 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.