Comptes Rendus
no. 6
A more applicable notion of effective stability for Hamiltonian systems
[Une notion plus applicable de stabilité effective pour les systèmes hamiltoniens]
Abed Bounemoura1
1 Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 401-404.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2012.02.024
Keywords: Dynamical systems, Hamiltonian systems, Effective stability
Mot clés : Systèmes dynamiques, Systèmes hamiltoniens, Stabilité effective
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/

[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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