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Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 72–106 (Mi tm3752)  

This article is cited in 1 scientific paper (total in 1 paper)

Arnold diffusion in a neighborhood of strong resonances

M. N. Davletshin, D. V. Treschev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: The paper deals with nearly integrable multidimensional a priori unstable Hamiltonian systems. Assuming the Hamilton function is smooth and time-periodic, we study perturbations that are trigonometric polynomials in the “angle” variables in the first approximation. For a generic system in this class, we construct a trajectory whose projection on the space of slow variables crosses a small neighborhood of a strong resonance. We also estimate the speed of this crossing.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516040051

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 63–94

Bibliographic databases:

Document Type: Article
UDC: 517.958+531.01
Received: May 29, 2016

Citation: M. N. Davletshin, D. V. Treschev, “Arnold diffusion in a neighborhood of strong resonances”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 72–106; Proc. Steklov Inst. Math., 295 (2016), 63–94

Citation in format AMSBIB
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\pages 72--106
\publ MAIK Nauka/Interperiodica
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  • http://mi.mathnet.ru/eng/tm3752
  • https://doi.org/10.1134/S0371968516040051
  • http://mi.mathnet.ru/eng/tm/v295/p72

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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. A. Delshams, R. G. Schaefer, “Arnold diffusion for a complete family of perturbations with two independent harmonics”, Discrete Contin. Dyn. Syst., 38:12 (2018), 6047–6072  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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