Generic Nekhoroshev theory without small divisors

TL;DR

This paper introduces a novel approach to Nekhoroshev theory that circumvents small divisors issues, enabling stability analysis of generic non-analytic Hamiltonians around linearly stable tori.

Contribution

It extends Lochak's method by removing small divisors constraints, allowing for broader applicability to generic non-analytic Hamiltonians.

Findings

Achieves stability results for generic non-analytic Hamiltonians.

Provides a new geometric approach to Nekhoroshev theory.

Handles generic integrable Hamiltonians without small divisors.

Abstract

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.