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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 72–106
DOI: https://doi.org/10.1134/S0371968516040051 (Mi tm3752) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (419 kB) Citations (3)
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DOI: https://doi.org/10.1134/S0371968516040051
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.
Received: May 29, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 63–94
DOI: https://doi.org/10.1134/S0081543816080058
Bibliographic databases:
Document Type: Article
UDC: 517.958+531.01
Language: Russian
Citation: M. N. Davletshin, D. V. Treschev, “Arnold diffusion in a neighborhood of strong resonances”, Modern problems of mechanics, Collected papers, Trudy 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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\paper Arnold diffusion in a~neighborhood of strong resonances
\inbook Modern problems of mechanics
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\vol 295
\pages 72--106
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968516040051}
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  • https://doi.org/10.1134/S0371968516040051
  • https://www.mathnet.ru/eng/tm/v295/p72
    • This publication is cited in the following 3 articles:
    1. A. Delshams, A. Granados, R. G. Schaefer, “Arnold diffusion for an a priori unstable Hamiltonian system with 3 + 1/2 degrees of freedom”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:6 (2024)  crossref
    2. Valery Kozlov, “On the diffusion mechanism in Hamiltonian systems”, Funct. Anal. Appl., 58:4 (2024), 362–370  mathnet  crossref  crossref
    3. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Abstract page:491
    Full-text PDF :132
    References:72
    First page:24
     
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