Email this article Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics
- Authors: Kuznetsov S.P.1,2,3, Kruglov V.P.2,3
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Affiliations:
- Udmurt State University
- Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch
- Saratov State University
- Issue: Vol 21, No 2 (2016)
- Pages: 160-174
- Section: Article
- URL: https://ogarev-online.ru/1560-3547/article/view/218238
- DOI: https://doi.org/10.1134/S1560354716020027
- ID: 218238
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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.
About the authors
Sergey P. Kuznetsov
Udmurt State University; Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch; Saratov State University
Author for correspondence.
Email: spkuz@yandex.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034; ul. Zelenaya 38, Saratov, 410019; ul. Astrakhanskaya 83, Saratov, 410012
Vyacheslav P. Kruglov
Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch; Saratov State University
Email: spkuz@yandex.ru
Russian Federation, ul. Zelenaya 38, Saratov, 410019; ul. Astrakhanskaya 83, Saratov, 410012
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