Title: Chaos in three coupled rotators: From Anosov dynamics to hyperbolic attractors,
Abstract: Starting from Anosov chaotic dynamics of geodesic flow on a surface of
negative curvature, we develop and consider a number of self-oscillatory
systems including those with hinged mechanical coupling of three rotators and a
system of rotators interacting through a potential function. These results are
used to design an electronic circuit for generation of rough (structurally
stable) chaos. Results of numerical integration of the model equations of
different degree of accuracy are presented and discussed. Also, circuit
simulation of the electronic generator is provided using the NI Multisim
environment. Portraits of attractors, waveforms of generated oscillations,
Lyapunov exponents, and spectra are considered and found to be in good
correspondence for the dynamics on the attractive sets of the self-oscillatory
systems and for the original Anosov geodesic flow. The hyperbolic nature of the
dynamics is tested numerically using a criterion based on statistics of angles
of intersection of stable and unstable subspaces of the perturbation vectors at
a reference phase trajectory on the attractor.