On persistence of invariant tori and a theorem by Nekhoroshev

Abstract

We give a proof of a theorem by N.N. Nekhoroshev concerning Hamiltonian systems with $n$ degrees of freedom and $s$ integrals of motion in involution, where $1\le s\le n$. Such a theorem ensures persistence of $s$-dimensional invariant tori under suitable nondegeneracy conditions generalizing Poincaré's condition on the Floquet multipliers.

13 pages, no figures