[Stabilité effective pour des hamiltoniens presque intégrables lentement non autonomes et application]
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.
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@article{CRMATH_2013__351_17-18_673_0,
author = {Bounemoura, Abed},
title = {Effective stability for slow time-dependent near-integrable {Hamiltonians} and application},
journal = {Comptes Rendus. Math\'ematique},
pages = {673--676},
publisher = {Elsevier},
volume = {351},
number = {17-18},
year = {2013},
doi = {10.1016/j.crma.2013.07.024},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.07.024/}
}
TY - JOUR AU - Bounemoura, Abed TI - Effective stability for slow time-dependent near-integrable Hamiltonians and application JO - Comptes Rendus. Mathématique PY - 2013 SP - 673 EP - 676 VL - 351 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.07.024/ DO - 10.1016/j.crma.2013.07.024 LA - en ID - CRMATH_2013__351_17-18_673_0 ER -
%0 Journal Article %A Bounemoura, Abed %T Effective stability for slow time-dependent near-integrable Hamiltonians and application %J Comptes Rendus. Mathématique %D 2013 %P 673-676 %V 351 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.07.024/ %R 10.1016/j.crma.2013.07.024 %G en %F CRMATH_2013__351_17-18_673_0
Bounemoura, Abed. Effective stability for slow time-dependent near-integrable Hamiltonians and application. Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 673-676. doi : 10.1016/j.crma.2013.07.024. http://www.numdam.org/articles/10.1016/j.crma.2013.07.024/
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