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This article is cited in 5 scientific papers (total in 5 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 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
DOI: https://doi.org/10.1134/S1560354716020027   References:
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MSC: 37D20, 37D45, 70G60, 70Q05 Received: 06.12.2015 Accepted:15.02.2016 Language: 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), 
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Citing articles on Google Scholar: Russian citations, English citations Related articles on Google Scholar: Russian articles, English articles This publication is cited in the following articles:
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