Generic Nekhoroshev theory without small divisors

Abed Bounemoura[1]; Laurent Niederman[1]

  • [1] Université Paris-Sud 11 Faculté des Sciences d’Orsay Département de Mathématiques Bâtiment 425 91405 Orsay cedex (France)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 277-324
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bounemoura, Abed, and Niederman, Laurent. "Generic Nekhoroshev theory without small divisors." Annales de l’institut Fourier 62.1 (2012): 277-324. <http://eudml.org/doc/251101>.

@article{Bounemoura2012,
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.},
affiliation = {Université Paris-Sud 11 Faculté des Sciences d’Orsay Département de Mathématiques Bâtiment 425 91405 Orsay cedex (France); Université Paris-Sud 11 Faculté des Sciences d’Orsay Département de Mathématiques Bâtiment 425 91405 Orsay cedex (France)},
author = {Bounemoura, Abed, Niederman, Laurent},
journal = {Annales de l’institut Fourier},
keywords = {Hamiltonian systems; perturbation of integrable systems; effective stability; small divisor problem},
language = {eng},
number = {1},
pages = {277-324},
publisher = {Association des Annales de l’institut Fourier},
title = {Generic Nekhoroshev theory without small divisors},
url = {http://eudml.org/doc/251101},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Bounemoura, Abed
AU - Niederman, Laurent
TI - Generic Nekhoroshev theory without small divisors
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 277
EP - 324
AB - 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.
LA - eng
KW - Hamiltonian systems; perturbation of integrable systems; effective stability; small divisor problem
UR - http://eudml.org/doc/251101
ER -

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