Generic super-exponential stability of invariant tori in Hamiltonian systems

Details Generic super-exponential stability of invariant tori in Hamiltonian systems Generic super-exponential stability of invariant tori in Hamiltonian systems

2009-12-18

arxiv.org/abs/0912.3600v2

Mathematics

Dynamical Systems

Scientific paper

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.

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