A more applicable notion of effective stability for Hamiltonian systems

Abed Bounemoura

doi:10.1016/j.crme.2012.02.024

A more applicable notion of effective stability for Hamiltonian systems

Abed Bounemoura ¹

¹ Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA

Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 401-404.

Abstract (Original language)
Résumé

The purpose of this Note is to give a result of effective stability for perturbations of integrable Hamiltonian systems, which we believe is more suitable for applications to concrete Hamiltonian systems.

Le but de cette Note est de donner un résultat de stabilité effective pour les perturbations de systèmes hamiltoniens intégrables, que nous pensons être plus adapté à des systèmes hamiltoniens concrets.

Received: 2011-10-28
Accepted: 2012-02-29
Published online: 2012-03-15

DOI: 10.1016/j.crme.2012.02.024

Keywords: Dynamical systems, Hamiltonian systems, Effective stability
Mots-clés : Systèmes dynamiques, Systèmes hamiltoniens, Stabilité effective

Author's affiliations:

Abed Bounemoura ¹

¹ Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA

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Abed Bounemoura. A more applicable notion of effective stability for Hamiltonian systems. Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 401-404. doi : 10.1016/j.crme.2012.02.024. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.024/

References
Cited by

[1] A.N. Kolmogorov On the preservation of conditionally periodic motions for a small change in Hamiltonʼs function, Dokl. Akad. Nauk SSSR, Volume 98 (1954), pp. 527-530

[2] N.N. Nekhoroshev An exponential estimate of the time of stability of nearly integrable Hamiltonian systems, Russian Math. Surveys, Volume 32 (1977) no. 6, pp. 1-65

[3] L. Niederman Stability over exponentially long times in the planetary problem, Nonlinearity, Volume 9 (1996) no. 6, pp. 1703-1751

[4] A. Bounemoura; J.-P. Marco Improved exponential stability for near-integrable Hamiltonian systems, Nonlinearity, Volume 24 (2011) no. 1, pp. 97-112

[5] J. Pöschel Nekhoroshev estimates for quasi-convex Hamiltonian systems, Math. Z., Volume 213 (1993), pp. 187-216

[6] A. Bounemoura, J.-P. Marco, L. Niederman, Stability estimates for the planetary problem, in preparation.

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