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

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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• http://mi.mathnet.ru/eng/tm3752
• https://doi.org/10.1134/S0371968516040051
• http://mi.mathnet.ru/eng/tm/v295/p72

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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
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