---
_id: '8495'
abstract:
- lang: eng
  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.'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Abed
  full_name: Bounemoura, Abed
  last_name: Bounemoura
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  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>
  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>
  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.
  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.
  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>.
  short: A. Bounemoura, V. Kaloshin, Proceedings of the American Mathematical Society
    144 (2015) 1553–1560.
date_created: 2020-09-18T10:46:14Z
date_published: 2015-12-21T00:00:00Z
date_updated: 2021-01-12T08:19:40Z
day: '21'
doi: 10.1090/proc/12796
extern: '1'
intvolume: '       144'
issue: '4'
language:
- iso: eng
month: '12'
oa_version: None
page: 1553-1560
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A note on micro-instability for Hamiltonian systems close to integrable
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2015'
...