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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 435–455 (Mi mmj474)  

This article is cited in 6 scientific papers (total in 6 papers)

KAM theory for lower dimensional tori within the reversible context 2

Mikhail B. Sevryuk

Institute of Energy Problems of Chemical Physics, The Russia Academy of Sciences, Leninskiĭ prospect 38, Bldg. 2, Moscow 119334, Russia

Abstract: The reversible context 2 in KAM theory refers to the situation where $\mathrm{dim} \mathrm{Fix}  G<\frac{1}{2}\mathrm{codim} \mathcal{T}$, here $\mathrm{Fix}  G$ is the fixed point manifold of the reversing involution $G$ and $\mathcal{T}$ is the invariant torus one deals with. Up to now, the persistence of invariant tori in the reversible context 2 has been only explored in the extreme particular case where $\mathrm{dim} \mathrm{Fix} G=0$ [M. B. Sevryuk, Regul. Chaotic Dyn. 16 (2011), no. 1–2, 24–38]. We obtain a KAM-type result for the reversible context 2 in the general situation where the dimension of $\mathrm{Fix}  G$ is arbitrary. As in the case where $\mathrm{dim} \mathrm{Fix}  G=0$, the main technical tool is J. Moser's modifying terms theorem of 1967.

Key words and phrases: KAM theory, Moser's modifying terms theorem, reversible systems, reversible context 2, fixed point manifold, lower dimensional invariant torus.

DOI: https://doi.org/10.17323/1609-4514-2012-12-2-435-455

Full text: http://www.ams.org/.../abst12-2-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 70K43, 70H33
Received: August 24, 2011
Language:

Citation: Mikhail B. Sevryuk, “KAM theory for lower dimensional tori within the reversible context 2”, Mosc. Math. J., 12:2 (2012), 435–455

Citation in format AMSBIB
\Bibitem{Sev12}
\by Mikhail~B.~Sevryuk
\paper KAM theory for lower dimensional tori within the reversible context~2
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 435--455
\mathnet{http://mi.mathnet.ru/mmj474}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-2-435-455}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978764}
\zmath{https://zbmath.org/?q=an:06126181}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309365900012}


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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, “Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory”, Regul. Chaotic Dyn., 21:6 (2016), 599–620  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
    4. Zh. Lou, J. Si, “Quasi-periodic solutions for the reversible derivative nonlinear Schrodinger equations with periodic boundary conditions”, J. Dyn. Differ. Equ., 29:3 (2017), 1031–1069  crossref  mathscinet  zmath  isi  scopus
    5. Zhang D., Xu J., Wang X., “A New Kam Iteration With Nearly Infinitely Small Steps in Reversible Systems of Polynomial Character”, Qual. Theor. Dyn. Syst., 17:1 (2018), 271–289  crossref  mathscinet  zmath  isi  scopus
    6. Hong W., Zhang D., “Persistence of Lower Dimensional Invariant Tori in a Class of Reversible Systems”, Dynam. Syst., 33:1 (2018), 72–92  crossref  mathscinet  zmath  isi  scopus
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