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Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics

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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.

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Authors and Affiliations

  1. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Sergey P. Kuznetsov

  2. Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia

    Sergey P. Kuznetsov & Vyacheslav P. Kruglov

  3. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    Sergey P. Kuznetsov & Vyacheslav P. Kruglov

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  1. Sergey P. Kuznetsov
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  2. Vyacheslav P. Kruglov
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Correspondence to Sergey P. Kuznetsov.

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Kuznetsov, S.P., Kruglov, V.P. Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics. Regul. Chaot. Dyn. 21, 160–174 (2016). https://doi.org/10.1134/S1560354716020027

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  • DOI: https://doi.org/10.1134/S1560354716020027

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