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Regular and Chaotic Dynamics

, Volume 21, Issue 2, pp 160–174 | Cite as

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

  • Sergey P. Kuznetsov
  • Vyacheslav P. Kruglov
Article

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 

MSC2010 numbers

37D20 37D45 70G60 70Q05 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Sergey P. Kuznetsov
    • 1
    • 2
    • 3
  • Vyacheslav P. Kruglov
    • 2
    • 3
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov BranchSaratovRussia
  3. 3.Saratov State UniversitySaratovRussia

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