On some simple examples of mechanical systems with hyperbolic chaos

Examples of mechanical systems with hyperbolic chaos are discussed, including the Thurston–Weeks–Hunt–MacKay hinge mechanism, in which conservative Anosov dynamics is realized, and dissipative systems with Smale–Williams type attractors (a particle on a plane under periodic kicks, interacting partic...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 297; no. 1; pp. 208 - 234
Main Authors Kuznetsov, S. P., Kruglov, V. P.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2017
Springer Nature B.V
Subjects
Dissipation
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Mechanical systems
Rotating disks
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Summary:Examples of mechanical systems with hyperbolic chaos are discussed, including the Thurston–Weeks–Hunt–MacKay hinge mechanism, in which conservative Anosov dynamics is realized, and dissipative systems with Smale–Williams type attractors (a particle on a plane under periodic kicks, interacting particles sliding on two alternately rotating disks, and a string with parametric excitation by modulated pump). The examples considered in the paper are interesting from the viewpoint of filling hyperbolic theory, as a well-developed field of the mathematical theory of dynamical systems, with physical content. The results of computer tests for hyperbolicity of the systems are presented that are based on the analysis of the statistics of intersection angles of stable and unstable manifolds.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543817040137