Torus actions and automorphism groups of singularities of integrable dynamical systems

Abstract

We show that in the neighborhood of each ``finite type'' singular orbit of a real analytic integrable dynamical system (hamiltonian or not) there is a real analytic torus action which preserves the system and which is transitive on this orbit. We also show that the local automorphism group of the system near such an orbit is

revised version, submitted to Comptes Rendus Acad Sci Paris