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Abed Bounemoura; Laurent Niederman
Generic Nekhoroshev theory without small divisors
(Théorie de Nekhoroshev générique sans petits diviseurs)
Annales de l'institut Fourier, 62 no. 1 (2012), p. 277-324, doi: 10.5802/aif.2706
Article PDF | Reviews MR 2986272 | Zbl 1257.37036
Class. Math.: 37J25, 37J40, 70H08, 70H09, 70K45, 70K60, 70K65
Keywords: Hamiltonian systems, perturbation of integrable systems, effective stability

Résumé - Abstract

In this article, we present a new approach of Nekhoroshev’s theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak, it 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.

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