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Regul. Chaotic Dyn., 2000, Volume 5, Issue 4, Pages 401–412 (Mi rcd887)  

This article is cited in 8 scientific papers (total in 8 papers)

Remarks on the Definition of Hyperbolic Tori of Hamiltonian Systems

S. V. Bolotin, D. V. Treschev

Department of Mathematics and Mechanics, Moscow State University, Vorob'evy Gory, 119899, Moscow, Russia

Abstract: We show that under certain natural conditions the definition of a hyperbolic torus conventional for the general theory of dynamical systems is quite suitable for needs of the KAM-theory.

DOI: https://doi.org/10.1070/RD2000v005n04ABEH000156


Bibliographic databases:

MSC: 58F05, 58F08
Received: 31.07.2000
Language:

Citation: S. V. Bolotin, D. V. Treschev, “Remarks on the Definition of Hyperbolic Tori of Hamiltonian Systems”, Regul. Chaotic Dyn., 5:4 (2000), 401–412

Citation in format AMSBIB
\Bibitem{BolTre00}
\by S. V. Bolotin, D. V. Treschev
\paper Remarks on the Definition of Hyperbolic Tori of Hamiltonian Systems
\jour Regul. Chaotic Dyn.
\yr 2000
\vol 5
\issue 4
\pages 401--412
\mathnet{http://mi.mathnet.ru/rcd887}
\crossref{https://doi.org/10.1070/RD2000v005n04ABEH000156}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1810623}
\zmath{https://zbmath.org/?q=an:1005.70015}


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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. M. B. Sevryuk, “The classical KAM theory at the dawn of the twenty-first century”, Mosc. Math. J., 3:3 (2003), 1113–1144  mathnet  crossref  mathscinet  zmath
    2. Abed Bounemoura, “Normal Forms, Stability and Splitting of Invariant Manifolds I. Gevrey Hamiltonians”, Regul. Chaotic Dyn., 18:3 (2013), 237–260  mathnet  crossref  mathscinet  zmath
    3. A. G. Medvedev, “Hyperbolic tori in Hamiltonian systems with slowly varying parameter”, Sb. Math., 204:5 (2013), 661–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. G. Medvedev, “Conservation of Hyperbolic Tori in Hamiltonian Systems”, Math. Notes, 95:2 (2014), 208–213  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Trans. Moscow Math. Soc., 76:2 (2015), 271–299  mathnet  crossref  elib
    6. S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. M. N. Davletshin, D. V. Treschev, “Arnold diffusion in a neighborhood of strong resonances”, Proc. Steklov Inst. Math., 295 (2016), 63–94  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Calleja R.C., Celletti A., de la Llave R., “Existence of Whiskered Kam Tori of Conformally Symplectic Systems”, Nonlinearity, 33:1 (2020), 538–597  crossref  mathscinet  zmath  isi  scopus
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