A note on micro-instability for Hamiltonian systems close to integrable - Archive ouverte HAL
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2016

A note on micro-instability for Hamiltonian systems close to integrable

Résumé

In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under generic assumptions on h and f , there exists an orbit of the system for which the drift of its action variables is at least of order square root of epsilon, after a time of order the inverse of square root of epsilon. The assumptions, which are essentially minimal, are that there exists a resonant point for h and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting.
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Dates et versions

hal-01098313 , version 1 (23-12-2014)
hal-01098313 , version 2 (09-01-2015)

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Abed Bounemoura, Vadim Kaloshin. A note on micro-instability for Hamiltonian systems close to integrable. Proceedings of the American Mathematical Society, 2016, 144 (4), pp.1553-1560. ⟨hal-01098313v2⟩
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