Generic super-exponential stability of invariant tori in Hamiltonian systems

Abstract

AbstractIn this article, we consider solutions that start 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 with a new method for obtaining generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will focus mainly on the neighbourhood of elliptic fixed points, since with our approach the other cases can be treated in a very similar way.