On persistence of invariant tori and a theorem by Nekhoroshev

摘要

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