94-319 G. Gaeta
Splitting equivariant dynamics (39K, TeX) Oct 14, 94
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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.

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