A note on micro-instability for Hamiltonian systems close to integrable
Bounemoura, Abed; Kaloshin, Vadim (2016), A note on micro-instability for Hamiltonian systems close to integrable, Proceedings of the American Mathematical Society, 144, p. 1553-1560. 10.1090/proc/12796
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1412.7455v2
Journal nameProceedings of the American Mathematical Society
American Mathematical Society
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Abstract (EN)In this note, we consider the dynamics associated to a perturbation of an integrableHamiltonian system in action-angle coordinates in any number of degrees of freedom andwe prove the following result of “micro-diffusion”: under generic assumptions onhandf,there exists an orbit of the system for which the drift of its action variables is at least oforder√ε, after a time of order√ε−1. The assumptions, which are essentially minimal, arethat there exists a resonant point forhand that the corresponding averaged perturbationis non-constant. The conclusions, although very weak when compared to usual instabilityphenomena, are also essentially optimal within this setting.
Subjects / KeywordsDynamical Systems
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