{"abstract":[{"text":"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.","lang":"eng"}],"_id":"8495","date_created":"2020-09-18T10:46:14Z","page":"1553-1560","publication_identifier":{"issn":["0002-9939","1088-6826"]},"month":"12","intvolume":"       144","publisher":"American Mathematical Society","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Bounemoura","full_name":"Bounemoura, Abed","first_name":"Abed"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"}],"day":"21","article_processing_charge":"No","title":"A note on micro-instability for Hamiltonian systems close to integrable","article_type":"letter_note","language":[{"iso":"eng"}],"doi":"10.1090/proc/12796","oa_version":"None","publication_status":"published","date_updated":"2021-01-12T08:19:40Z","issue":"4","status":"public","year":"2015","extern":"1","publication":"Proceedings of the American Mathematical Society","type":"journal_article","volume":144,"date_published":"2015-12-21T00:00:00Z","citation":{"apa":"Bounemoura, A., &#38; Kaloshin, V. (2015). A note on micro-instability for Hamiltonian systems close to integrable. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/12796\">https://doi.org/10.1090/proc/12796</a>","ama":"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>","ista":"Bounemoura A, Kaloshin V. 2015. A note on micro-instability for Hamiltonian systems close to integrable. Proceedings of the American Mathematical Society. 144(4), 1553–1560.","short":"A. Bounemoura, V. Kaloshin, Proceedings of the American Mathematical Society 144 (2015) 1553–1560.","chicago":"Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for Hamiltonian Systems Close to Integrable.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2015. <a href=\"https://doi.org/10.1090/proc/12796\">https://doi.org/10.1090/proc/12796</a>.","ieee":"A. Bounemoura and V. Kaloshin, “A note on micro-instability for Hamiltonian systems close to integrable,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4. American Mathematical Society, pp. 1553–1560, 2015.","mla":"Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for Hamiltonian Systems Close to Integrable.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4, American Mathematical Society, 2015, pp. 1553–60, doi:<a href=\"https://doi.org/10.1090/proc/12796\">10.1090/proc/12796</a>."}}