Smooth normal forms for integrable hamiltonian systems near a focus-focus singularity

San Vu Ngoc (1) , Christophe Wacheux (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that completely integrable systems are normalisable in the C infinity category near focus-focus singularities.

Mots clés: normal form; focus-focus singularity; Liouville integrable system

Domaines: Géométrie symplectique [math.SG]

San Vu Ngoc, Christophe Wacheux. Smooth normal forms for integrable hamiltonian systems near a focus-focus singularity. Acta Mathematica Vietnamica, 2013, 38 (1), pp.107-122. ⟨10.1007/s40306-013-0012-5⟩. ⟨hal-00577205⟩