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Regular and Chaotic Dynamics, 2019, Volume 24, Issue 6, Pages 583–606
DOI: https://doi.org/10.1134/S1560354719060017 (Mi rcd1027) 		 
This article is cited in 7 scientific papers (total in 7 papers)

V. I. Arnold's "Pointwise" KAM Theorem

L. Chierchia, C. E. Koudjinan

Dipartimento di Matematica, Università Roma Tre, Largo S. L. Murialdo 1, I-00146 Roma, Italy
Citations (7)
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DOI: https://doi.org/10.1134/S1560354719060017
Abstract: We review V. I. Arnold's 1963 celebrated paper [1] Proof of A. N. Kolmogorov's Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold's scheme, one can get “sharp” asymptotic quantitative conditions (as $\varepsilon \to 0$, $\varepsilon$ being the strength of the perturbation). All constants involved are explicitly computed.
Keywords: Nearly-integrable Hamiltonian systems, KAM theory, Arnold's Theorem, small divisors, perturbation theory, symplectic transformations.
Funding agency Grant number
European Research Council 306414
L. C. has been supported by the ERC grant HamPDEs under FP7 no. 306414 and the PRIN national grant “Variational Methods in Analysis, Geometry and Physics”.
Received: 11.09.2019
Accepted: 11.10.2019
Bibliographic databases:
Document Type: Article
MSC: 37J40, 37J05, 37J25, 70H08
Language: English
Citation: L. Chierchia, C. E. Koudjinan, “V. I. Arnold's "Pointwise" KAM Theorem”, Regul. Chaotic Dyn., 24:6 (2019), 583–606
Citation in format AMSBIB
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\by L. Chierchia, C. E. Koudjinan
\paper V. I. Arnold's ''Pointwise'' KAM Theorem
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 583--606
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\crossref{https://doi.org/10.1134/S1560354719060017}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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