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Matematicheskie Zametki, 2014, Volume 95, Issue 2, Pages 227–233
DOI: https://doi.org/10.4213/mzm10124 (Mi mzm10124) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Conservation of Hyperbolic Tori in Hamiltonian Systems

A. G. Medvedev

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm10124
Abstract: In 2000, Bolotin and Treshchev proposed an invariant definition of the hyperbolic torus, generalizing the traditional coordinate definition. Simultaneously, they conjectured that, under standard assumptions on its Diophantine properties, nondegeneracy, and analyticity, the hyperbolic torus is conserved in the case of small perturbations. This conjecture generalizes Graff's theorem. In the present paper, this conjecture is shown to be valid.
Keywords: hyperbolic torus, Hamiltonian system, Graff's theorem, Diophantine torus, frequency vector, KAM theory.
Received: 30.07.2012
Revised: 20.03.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 2, Pages 208–213
DOI: https://doi.org/10.1134/S0001434614010222
Bibliographic databases:
Document Type: Article
UDC: 517.933
Language: Russian
Citation: A. G. Medvedev, “Conservation of Hyperbolic Tori in Hamiltonian Systems”, Mat. Zametki, 95:2 (2014), 227–233; Math. Notes, 95:2 (2014), 208–213
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. E. A. Kudryavtseva, “Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the C1 Topology”, Math. Notes, 99:4 (2016), 611–615  mathnet  crossref  crossref  mathscinet  isi  elib
    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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