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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
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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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\pages 72--106
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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