A note on micro-instability for Hamiltonian systems close to integrable Bounemoura, Abed Kaloshin, Vadim ; https://orcid.org/0000-0002-6051-2628 In this note, we consider the dynamics associated to a 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 $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-1}$. 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. American Mathematical Society 2015 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://research-explorer.ista.ac.at/record/8495 Bounemoura A, Kaloshin V. A note on micro-instability for Hamiltonian systems close to integrable. <i>Proceedings of the American Mathematical Society</i>. 2015;144(4):1553-1560. doi:<a href="https://doi.org/10.1090/proc/12796">10.1090/proc/12796</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/12796 info:eu-repo/semantics/altIdentifier/issn/0002-9939 info:eu-repo/semantics/altIdentifier/issn/1088-6826 info:eu-repo/semantics/closedAccess