Résumé (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.