---
_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. Regular and Chaotic Dynamics. 2021;26(1):61-88. doi:10.1134/S1560354721010044
apa: Chierchia, L., & Koudjinan, E. (2021). V.I. Arnold’s “‘Global’” KAM theorem
and geometric measure estimates. Regular and Chaotic Dynamics. Springer
Nature. https://doi.org/10.1134/S1560354721010044
chicago: Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem
and Geometric Measure Estimates.” Regular and Chaotic Dynamics. Springer
Nature, 2021. https://doi.org/10.1134/S1560354721010044.
ieee: L. Chierchia and E. Koudjinan, “V.I. Arnold’s ‘“Global”’ KAM theorem and geometric
measure estimates,” Regular and Chaotic Dynamics, 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.” Regular and Chaotic Dynamics, vol. 26,
no. 1, Springer Nature, 2021, pp. 61–88, doi:10.1134/S1560354721010044.
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'
...
---
OA_place: repository
_id: '9435'
abstract:
- lang: eng
text: For any given positive integer l, we prove that every plane deformation of
a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e.
the deformationconsists only of similarities (rescalings and isometries).
article_number: '2107.03499'
article_processing_charge: No
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
citation:
ama: Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles. arXiv. doi:10.48550/arXiv.2107.03499
apa: Kaloshin, V., & Koudjinan, E. (n.d.). Non co-preservation of the 1/2 and
1/(2l+1)-rational caustics along deformations of circles. arXiv. https://doi.org/10.48550/arXiv.2107.03499
chicago: Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2
and 1/(2l+1)-Rational Caustics along Deformations of Circles.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2107.03499.
ieee: V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles,” arXiv. .
ista: Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles. arXiv, 2107.03499.
mla: Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and
1/(2l+1)-Rational Caustics along Deformations of Circles.” ArXiv, 2107.03499,
doi:10.48550/arXiv.2107.03499.
short: V. Kaloshin, E. Koudjinan, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-05-30T13:58:13Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2025-01-22T08:09:40Z
day: '07'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.48550/arXiv.2107.03499
external_id:
arxiv:
- '2107.03499'
file:
- access_level: open_access
checksum: b281b5c2e3e90de0646c3eafcb2c6c25
content_type: application/pdf
creator: ekoudjin
date_created: 2021-05-30T13:57:37Z
date_updated: 2021-05-30T13:57:37Z
file_id: '9436'
file_name: CoExistence 2&3 caustics 3_17_6_2_3.pdf
file_size: 353431
relation: main_file
file_date_updated: 2021-05-30T13:57:37Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2107.03499
month: '07'
oa: 1
oa_version: Submitted Version
publication: arXiv
publication_status: submitted
status: public
title: Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations
of circles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...