On some simple examples of mechanical systems with hyperbolic chaos


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Resumo

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.

Sobre autores

S. Kuznetsov

Udmurt State University; Saratov Branch of the Kotel’nikov Institute of Radio Engineering and Electronics; Saratov State University

Autor responsável pela correspondência
Email: spkuz@yandex.ru
Rússia, ul. Universitetskaya 1, Izhevsk, 426034; ul. Zelenaya 38, Saratov, 410019; ul. Astrakhanskaya 83, Saratov, 410012

V. Kruglov

Saratov Branch of the Kotel’nikov Institute of Radio Engineering and Electronics; Saratov State University

Email: spkuz@yandex.ru
Rússia, ul. Zelenaya 38, Saratov, 410019; ul. Astrakhanskaya 83, Saratov, 410012

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