---
_id: '8689'
abstract:
- lang: eng
  text: 'This paper continues the discussion started in [CK19] concerning Arnold''s
    legacy on classical KAM theory and (some of) its modern developments. We prove
    a detailed and explicit `global'' Arnold''s KAM Theorem, which yields, in particular,
    the Whitney conjugacy of a non{degenerate, real{analytic, nearly-integrable Hamiltonian
    system to an integrable system on a closed, nowhere dense, positive measure subset
    of the phase space. Detailed measure estimates on the Kolmogorov''s set are provided
    in the case the phase space is: (A) a uniform neighbourhood of an arbitrary (bounded)
    set times the d-torus and (B) a domain with C2 boundary times the d-torus. All
    constants are explicitly given.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Luigi
  full_name: Chierchia, Luigi
  last_name: Chierchia
- first_name: Edmond
  full_name: Koudjinan, Edmond
  id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
  last_name: Koudjinan
  orcid: 0000-0003-2640-4049
citation:
  ama: Chierchia L, Koudjinan E. V.I. Arnold’s “‘Global’” KAM theorem and geometric
    measure estimates. <i>Regular and Chaotic Dynamics</i>. 2021;26(1):61-88. doi:<a
    href="https://doi.org/10.1134/S1560354721010044">10.1134/S1560354721010044</a>
  apa: Chierchia, L., &#38; Koudjinan, E. (2021). V.I. Arnold’s “‘Global’” KAM theorem
    and geometric measure estimates. <i>Regular and Chaotic Dynamics</i>. Springer
    Nature. <a href="https://doi.org/10.1134/S1560354721010044">https://doi.org/10.1134/S1560354721010044</a>
  chicago: Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem
    and Geometric Measure Estimates.” <i>Regular and Chaotic Dynamics</i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1134/S1560354721010044">https://doi.org/10.1134/S1560354721010044</a>.
  ieee: L. Chierchia and E. Koudjinan, “V.I. Arnold’s ‘“Global”’ KAM theorem and geometric
    measure estimates,” <i>Regular and Chaotic Dynamics</i>, vol. 26, no. 1. Springer
    Nature, pp. 61–88, 2021.
  ista: Chierchia L, Koudjinan E. 2021. V.I. Arnold’s ‘“Global”’ KAM theorem and geometric
    measure estimates. Regular and Chaotic Dynamics. 26(1), 61–88.
  mla: Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem
    and Geometric Measure Estimates.” <i>Regular and Chaotic Dynamics</i>, vol. 26,
    no. 1, Springer Nature, 2021, pp. 61–88, doi:<a href="https://doi.org/10.1134/S1560354721010044">10.1134/S1560354721010044</a>.
  short: L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 26 (2021) 61–88.
date_created: 2020-10-21T14:56:47Z
date_published: 2021-02-03T00:00:00Z
date_updated: 2023-08-07T13:37:27Z
day: '03'
ddc:
- '515'
department:
- _id: VaKa
doi: 10.1134/S1560354721010044
external_id:
  arxiv:
  - '2010.13243'
  isi:
  - '000614454700004'
intvolume: '        26'
isi: 1
issue: '1'
keyword:
- Nearly{integrable Hamiltonian systems
- perturbation theory
- KAM Theory
- Arnold's scheme
- Kolmogorov's set
- primary invariant tori
- Lagrangian tori
- measure estimates
- small divisors
- integrability on nowhere dense sets
- Diophantine frequencies.
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2010.13243
month: '02'
oa: 1
oa_version: Preprint
page: 61-88
publication: Regular and Chaotic Dynamics
publication_identifier:
  issn:
  - 1560-3547
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2021'
...