---
_id: '8494'
abstract:
- lang: eng
  text: "We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe
    a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly
    convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere
    l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance,
    and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor
    the proof we use a combination of geometric and variational methods, and manage
    to adapt tools which have recently been developed in the a-priori unstable case."
article_processing_charge: No
article_type: original
author:
- first_name: Patrick
  full_name: Bernard, Patrick
  last_name: Bernard
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Ke
  full_name: Zhang, Ke
  last_name: Zhang
citation:
  ama: Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom
    and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. 2016;217(1):1-79.
    doi:<a href="https://doi.org/10.1007/s11511-016-0141-5">10.1007/s11511-016-0141-5</a>
  apa: Bernard, P., Kaloshin, V., &#38; Zhang, K. (2016). Arnold diffusion in arbitrary
    degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>.
    Institut Mittag-Leffler. <a href="https://doi.org/10.1007/s11511-016-0141-5">https://doi.org/10.1007/s11511-016-0141-5</a>
  chicago: Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary
    Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>.
    Institut Mittag-Leffler, 2016. <a href="https://doi.org/10.1007/s11511-016-0141-5">https://doi.org/10.1007/s11511-016-0141-5</a>.
  ieee: P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees
    of freedom and normally hyperbolic invariant cylinders,” <i>Acta Mathematica</i>,
    vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.
  ista: Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees
    of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1),
    1–79.
  mla: Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom
    and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>, vol. 217,
    no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:<a href="https://doi.org/10.1007/s11511-016-0141-5">10.1007/s11511-016-0141-5</a>.
  short: P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79.
date_created: 2020-09-18T10:46:07Z
date_published: 2016-09-28T00:00:00Z
date_updated: 2021-01-12T08:19:39Z
day: '28'
doi: 10.1007/s11511-016-0141-5
extern: '1'
fulldoi: https://doi.org/10.1007/s11511-016-0141-5
intvolume: '       217'
issue: '1'
language:
- iso: eng
month: '09'
oa_version: None
page: 1-79
publication: Acta Mathematica
publication_identifier:
  issn:
  - 0001-5962
publication_status: published
publisher: Institut Mittag-Leffler
quality_controlled: '1'
status: public
title: Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant
  cylinders
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 217
year: '2016'
...