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Matematicheskie Zametki, 1997, Volume 61, Issue 6, Pages 890–906
DOI: https://doi.org/10.4213/mzm1573
(Mi mzm1573)
 

This article is cited in 4 scientific papers (total in 4 papers)

Separatrix splitting from the point of view of symplectic geometry

D. V. Treschev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (434 kB) Citations (4)
References:
Abstract: Generally, the invariant Lagrangian manifolds (stable and unstable separatrices) asymptotic with respect to a hyperbolic torus of a Hamiltonian system do not coincide. This phenomenon is called separatrix splitting. In this paper, a symplectic invariant qualitatively describing separatrix splitting for hyperbolic tori of maximum (smaller by one than the number of degrees of freedom) dimension is constructed. The construction resembles that of the homoclinic invariant found by Lazutkin for two-dimensional symplectic maps and of Bolotin's invariant for splitting of asymptotic manifolds of a fixed point of a symplectic diffeomorphism.
Received: 27.06.1995
English version:
Mathematical Notes, 1997, Volume 61, Issue 6, Pages 744–757
DOI: https://doi.org/10.1007/BF02361217
Bibliographic databases:
Document Type: Article
UDC: 514.154
Language: Russian
Citation: D. V. Treschev, “Separatrix splitting from the point of view of symplectic geometry”, Mat. Zametki, 61:6 (1997), 890–906; Math. Notes, 61:6 (1997), 744–757
Citation in format AMSBIB
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\by D.~V.~Treschev
\paper Separatrix splitting from the point of view of symplectic geometry
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 6
\pages 890--906
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\crossref{https://doi.org/10.4213/mzm1573}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1629817}
\zmath{https://zbmath.org/?q=an:0915.58031}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 744--757
\crossref{https://doi.org/10.1007/BF02361217}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997YE52200029}
Linking options:
  • https://www.mathnet.ru/eng/mzm1573
  • https://doi.org/10.4213/mzm1573
  • https://www.mathnet.ru/eng/mzm/v61/i6/p890
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    Abstract page:599
    Full-text PDF :294
    References:64
    First page:3
     
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