Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: testing absence of tangencies of stable and unstable manifolds for phase trajectories

DOI10.1134/S1560354715060027zbMath1344.37046arXiv1510.03593MaRDI QIDQ283349

Sergey P. Kuznetsov

Publication date: 13 May 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.03593

zbMATH Keywords

chaosdynamical systemLyapunov exponenthyperbolic attractorAnosov dynamicsrotatorself-oscillator

Mathematics Subject Classification ID

Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Simulation of dynamical systems (37M05) Holonomic systems related to the dynamics of a system of particles (70F20) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Negative curvature complex manifolds (32Q05)

Related Items

Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics ⋮ On some simple examples of mechanical systems with hyperbolic chaos ⋮ Chaos and hyperchaos of geodesic flows on curved manifolds corresponding to mechanically coupled rotators: Examples and numerical study ⋮ From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos ⋮ Numerical test for hyperbolicity in chaotic systems with multiple time delays ⋮ Hyperbolic chaos in a system of two Froude pendulums with alternating periodic braking

Cites Work

• Plate falling in a fluid: regular and chaotic dynamics of finite-dimensional models
• Example of blue sky catastrophe accompanied by a birth of Smale-Williams attractor
• Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: numerical test for expanding and contracting cones
• An equation for hyperchaos
• Hyperbolic and non-hyperbolic chaos in a pair of coupled alternately excited FitzHugh-Nagumo systems
• Studying hyperbolicity in chaotic systems
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• Lectures on partial hyperbolicity and stable ergodicity
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Geometry and dynamics of planar linkages
• Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback
• Autonomous coupled oscillators with hyperbolic strange attractors
• Hyperbolic Chaos
• How often are chaotic saddles nonhyperbolic?
• On the motion of a heavy rigid body in an ideal fluid with circulation
• Mathematical Problems of Nonlinear Dynamics: A Tutorial
• Anosov parameter values for the triple linkage and a physical system with a uniformly chaotic attractor
• Plykin type attractor in electronic device simulated in <scp>MULTISIM</scp>
• Differentiable dynamical systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item