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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 2, Pages 160–174
DOI: https://doi.org/10.1134/S1560354716020027 (Mi rcd72) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics

Sergey P. Kuznetsovabc, Vyacheslav P. Kruglovcb

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia
c Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia
Citations (12)
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DOI: https://doi.org/10.1134/S1560354716020027
Abstract: Computer verification of hyperbolicity is provided based on statistical analysis of the angles of intersection of stable and unstable manifolds for mechanical systems with hyperbolic attractors of Smale – Williams type: (i) a particle sliding on a plane under periodic kicks, (ii) interacting particles moving on two alternately rotating disks, and (iii) a string with parametric excitation of standing-wave patterns by a modulated pump. The examples are of interest as contributing to filling the hyperbolic theory of dynamical systems with physical content.
Keywords: dynamical system, chaos, attractor, hyperbolic dynamics, Lyapunov exponent, Smale – Williams solenoid, parametric oscillations.
Funding agency Grant number
Russian Science Foundation 15-12-20035
This work was supported by RSF grant No 15-12-20035.
Received: 06.12.2015
Accepted: 15.02.2016
Bibliographic databases:
Document Type: Article
MSC: 37D20, 37D45, 70G60, 70Q05
Language: English
Citation: Sergey P. Kuznetsov, Vyacheslav P. Kruglov, “Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 160–174
Citation in format AMSBIB
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\by Sergey P. Kuznetsov, Vyacheslav P. Kruglov
\paper Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics
\jour Regul. Chaotic Dyn.
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\vol 21
\issue 2
\pages 160--174
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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