V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates

L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 26 (2021) 61–88.

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Journal Article | Published | English
Author
Chierchia, Luigi; Koudjinan, EdmondIST Austria
Department
Abstract
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.
Publishing Year
Date Published
2021-02-03
Journal Title
Regular and Chaotic Dynamics
Volume
26
Issue
1
Page
61-88
ISSN
IST-REx-ID

Cite this

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
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
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.
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.
Chierchia L, Koudjinan E. 2021. V.I. Arnold’s ‘“Global”’ KAM theorem and geometric measure estimates. Regular and Chaotic Dynamics. 26(1), 61–88.
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.

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