Nekhoroshev-Stability of Elliptic Equilibria of Hamiltonian Systems

Abstract:

We prove a conjecture by N.N. Nekhoroshev about the long-time stability of elliptic equilibria of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher order terms of the Hamiltonian are used to provide convexity. The singularity of the action-angle coordinates at the origin is overcome by working in cartesian coordinates.