Actions toriques et groupes d'automorphismes de singularités des systèmes dynamiques intégrables

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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 essentially Abelian. To cite this article: N.T. Zung, C. R. Acad. Sci. Paris, Ser. I 336 (2003).