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Regul. Chaotic Dyn., 2016, Volume 21, Issue 6, Pages 599–620 (Mi rcd212)  

This article is cited in 3 scientific papers (total in 3 papers)

Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory

Mikhail B. Sevryuk

V. L. Talroze Institute of Energy Problems of Chemical Physics of the Russian Academy of Sciences, Leninskii pr. 38, Building 2, Moscow, 119334 Russia

Abstract: We prove a general theorem on the persistence of Whitney $C^\infty$-smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where $\dim Fix  G < (codim\mathcal{T})/2$, where $Fix G$ is the fixed point manifold of the reversing involution $G$ and $\mathcal{T}$ is the invariant torus in question. Our result is obtained as a corollary of the theorem by H. W. Broer, M.-C. Ciocci, H. Hanßmann, and A. Vanderbauwhede (2009) concerning quasi-periodic stability of invariant tori with singular “normal” matrices in reversible systems.

Keywords: KAM theory, reversible systems, BCHV theorem, reversible context 2, invariant tori, Whitney smooth families

DOI: https://doi.org/10.1134/S1560354716060022

References: PDF file   HTML file

Bibliographic databases:

MSC: 70K43, 70H33
Received: 09.05.2016
Accepted:21.10.2016
Language:

Citation: Mikhail B. Sevryuk, “Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory”, Regul. Chaotic Dyn., 21:6 (2016), 599–620

Citation in format AMSBIB
\Bibitem{Sev16}
\by Mikhail B. Sevryuk
\paper Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 6
\pages 599--620
\mathnet{http://mi.mathnet.ru/rcd212}
\crossref{https://doi.org/10.1134/S1560354716060022}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3583939}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85006320079}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mikhail B. Sevryuk, “Families of Invariant Tori in KAM Theory: Interplay of Integer Characteristics”, Regul. Chaotic Dyn., 22:6 (2017), 603–615  mathnet  crossref  mathscinet
    2. M. B. Sevryuk, “Chastichnoe sokhranenie chastot i pokazatelei Floke invariantnykh torov v obratimom kontekste 2 teorii KAM”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 3, Rossiiskii universitet druzhby narodov, M., 2017, 516–541  mathnet  crossref
    3. Mikhail B. Sevryuk, “Herman's approach to quasi-periodic perturbations in the reversible KAM context 2”, Mosc. Math. J., 17:4 (2017), 803–823  mathnet  crossref
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