---
_id: '8414'
abstract:
- lang: eng
  text: "Arnold diffusion, which concerns the appearance of chaos in classical mechanics,
    is one of the most important problems in the fields of dynamical systems and mathematical
    physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted
    the efforts of some of the most prominent researchers in mathematics. The question
    is whether a typical perturbation of a particular system will result in chaotic
    or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and
    Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that
    that there is topological instability for typical perturbations of five-dimensional
    integrable systems (two and a half degrees of freedom).\r\nThis proof realizes
    a plan John Mather announced in 2003 but was unable to complete before his death.
    Kaloshin and Zhang follow Mather’s strategy but emphasize a more Hamiltonian approach,
    tying together normal forms theory, hyperbolic theory, Mather theory, and weak
    KAM theory. Offering a complete, clean, and modern explanation of the steps involved
    in the proof, and a clear account of background material, this book is designed
    to be accessible to students as well as researchers. The result is a critical
    contribution to mathematical physics and dynamical systems, especially Hamiltonian
    systems."
alternative_title:
- Annals of Mathematics Studies
article_processing_charge: No
author:
- 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: Kaloshin V, Zhang K. <i>Arnold Diffusion for Smooth Systems of Two and a Half
    Degrees of Freedom</i>. Vol 208. 1st ed. Princeton University Press; 2020. doi:<a
    href="https://doi.org/10.1515/9780691204932">10.1515/9780691204932</a>
  apa: Kaloshin, V., &#38; Zhang, K. (2020). <i>Arnold Diffusion for Smooth Systems
    of Two and a Half Degrees of Freedom</i> (1st ed., Vol. 208). Princeton University
    Press. <a href="https://doi.org/10.1515/9780691204932">https://doi.org/10.1515/9780691204932</a>
  chicago: Kaloshin, Vadim, and Ke Zhang. <i>Arnold Diffusion for Smooth Systems of
    Two and a Half Degrees of Freedom</i>. 1st ed. Vol. 208. AMS. Princeton University
    Press, 2020. <a href="https://doi.org/10.1515/9780691204932">https://doi.org/10.1515/9780691204932</a>.
  ieee: V. Kaloshin and K. Zhang, <i>Arnold Diffusion for Smooth Systems of Two and
    a Half Degrees of Freedom</i>, 1st ed., vol. 208. Princeton University Press,
    2020.
  ista: Kaloshin V, Zhang K. 2020. Arnold Diffusion for Smooth Systems of Two and
    a Half Degrees of Freedom 1st ed., Princeton University Press, 224p.
  mla: Kaloshin, Vadim, and Ke Zhang. <i>Arnold Diffusion for Smooth Systems of Two
    and a Half Degrees of Freedom</i>. 1st ed., vol. 208, Princeton University Press,
    2020, doi:<a href="https://doi.org/10.1515/9780691204932">10.1515/9780691204932</a>.
  short: V. Kaloshin, K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half
    Degrees of Freedom, 1st ed., Princeton University Press, 2020.
date_created: 2020-09-17T10:41:05Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2021-12-21T10:50:49Z
day: '01'
doi: 10.1515/9780691204932
edition: '1'
extern: '1'
intvolume: '       208'
language:
- iso: eng
month: '03'
oa_version: None
page: '224'
publication_identifier:
  isbn:
  - 9-780-6912-0253-2
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
scopus_import: '1'
series_title: AMS
status: public
title: Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
type: book
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 208
year: '2020'
...