A note on micro-instability for Hamiltonian systems close to integrable
Dynamical Systems
2015-01-12 v2
Abstract
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.
Cite
@article{arxiv.1412.7455,
title = {A note on micro-instability for Hamiltonian systems close to integrable},
author = {Abed Bounemoura and Vadim Kaloshin},
journal= {arXiv preprint arXiv:1412.7455},
year = {2015}
}