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Mat. Zametki, 2014, Volume 95, Issue 2, Pages 227–233 (Mi mz10124)  

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

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.

DOI: https://doi.org/10.4213/mzm10124

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English version:
Mathematical Notes, 2014, 95:2, 208–213

Bibliographic databases:

UDC: 517.933
Received: 30.07.2012
Revised: 20.03.2013

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Kudryavtseva, “Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the $C^1$ Topology”, Math. Notes, 99:4 (2016), 611–615  mathnet  crossref  crossref  mathscinet  isi  elib
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