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

被引：0
作者：
Sergey P. Kuznetsov
Vyacheslav P. Kruglov
机构：
[1] Udmurt State University,
[2] Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS,undefined
[3] Saratov Branch,undefined
[4] Saratov State University,undefined
来源：
Regular and Chaotic Dynamics | 2016年 / 21卷
关键词：
dynamical system; chaos; attractor; hyperbolic dynamics; Lyapunov exponent; Smale–Williams solenoid; parametric oscillations; 37D20; 37D45; 70G60; 70Q05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：160 / 174
页数：14
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