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 Tr. Mat. Inst. Steklova, 2017, Volume 297, Pages 232–259 (Mi tm3757)

On some simple examples of mechanical systems with hyperbolic chaos

S. P. Kuznetsovabc, V. P. Kruglovbc

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Saratov Branch of the Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, ul. Zelenaya 38, Saratov, 410019 Russia
c Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia

Abstract: 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.

 Funding Agency Grant Number Russian Science Foundation 15-12-20035 This work is supported by the Russian Science Foundation under grant 15-12-20035.

DOI: https://doi.org/10.1134/S0371968517020133

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 297, 208–234

Bibliographic databases:

UDC: 517.9+501+51-72+531.3+534.112+515.16

Citation: S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Tr. Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 232–259; Proc. Steklov Inst. Math., 297 (2017), 208–234

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3757
• https://doi.org/10.1134/S0371968517020133
• http://mi.mathnet.ru/eng/tm/v297/p232

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This publication is cited in the following articles:
1. S. P. Kuznetsov, “Khaos i giperkhaos geodezicheskikh potokov na mnogoobraziyakh s kriviznoi, otvechayuschikh mekhanicheski svyazannym rotatoram: primery i chislennoe issledovanie”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 565–581
2. Kuznetsov S.P., Kruglov V.P., “Hyperbolic Chaos in a System of Two Froude Pendulums With Alternating Periodic Braking”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 152–161
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