Generic super-exponential stability of invariant tori in Hamiltonian systems

Abed Bounemoura (1, 2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IMJ - Institut de Mathématiques de Jussieu

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Mots clés: Dynamical Systems; Hamiltonian Systems; Stability theory; Nekhoroshev theory

Domaines: Systèmes dynamiques [math.DS]

Abed Bounemoura. Generic super-exponential stability of invariant tori in Hamiltonian systems. Ergodic Theory and Dynamical Systems, 2011, 31 (5), pp.1287-1303. ⟨hal-00441994v2⟩