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In this note, we consider the dynamics associated to an epsilon-perturbationof an integrable Hamiltonian system in action-angle coordinates in any numberof 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 forwhich the drift of its action variables is at least of order square root ofepsilon, after a time of order the inverse of square root of epsilon. Theassumptions, which are essentially minimal, are that there exists a resonantpoint for h and that the corresponding averaged perturbation is non-constant.The conclusions, although very weak when compared to usual instabilityphenomena, are also essentially optimal within this setting.

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