Comptes Rendus
no. 17-18
Partial differential equations
Effective stability for slow time-dependent near-integrable Hamiltonians and application
[Stabilité effective pour des hamiltoniens presque intégrables lentement non autonomes et application]

Présenté par : the Editorial Board

Abed Bounemoura1
1 Institut des hautes études scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 673-676.

Le but de cette note est de démontrer un résultat de stabilité effective pour une perturbation non autonome dʼun système hamiltonien intégrable, sous la condition que la perturbation dépende lentement du temps. Nous utilisons ensuite ce résultat pour clarifier et généraliser un résultat de stabilité de Giorgilli et Zehnder pour des systèmes mécaniques dont le potentiel dépend arbitrairement du temps.

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.024
Abed Bounemoura 1

1 Institut des hautes études scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France 
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Abed Bounemoura. Effective stability for slow time-dependent near-integrable Hamiltonians and application. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 673-676. doi : 10.1016/j.crma.2013.07.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.024/

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