Titlebook: Hyperbolic Chaos; A Physicist’s View Sergey P. Kuznetsov Book 2012 Higher Education Press, Beijing and Springer-Verlag GmbH Berlin Heidelbe

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Parametric Generators of Hyperbolic Chaosters, may be regarded as some general principle of design of systems with attractors of the Smale-Williams type. Appropriate and convenient for implementation of this principle, are . (Mandelshtam, 1972; Louisell, 1960; Akhmanov and Khokhlov, 1966; Rabinovich and Trubetskov, 1989; Damgov, 2004), The

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Recognizing the Hyperbolicity: Cone Criterion and Other Approaches verification of the hyperbolicity in systems, which potentially may possess uniformly hyperbolic chaotic attractors. Substantiation of hyperbolicity is essential to accounting relevant conclusions of the mathematical theory, like availability of description in terms of Markov partitions with a fini

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Systems of Four Alternately Excited Non-autonomous Oscillatorser. In contrast to Chap. 4, here we examine dynamics in the phase space of larger dimensions; so, the models arc composed of four oscillators activating by turns (usually in pairs). Particularly, we consider a model, in which evolution of the phases in successive epochs of activity is described by t

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Systems with Time-delay Feedbackhis case, it is sufficient to have a single self-oscillator manifesting successive stages of activity and suppression, while the excitation transfer accompanied with appropriate phase transformation is carried out through the delayed feedback loop, from one stage of activity to another. In practical

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Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Mapsratory devices and studied in experiments described in (Kuznetsov and Ponomarenko, 2008; Baranov et al., 2010). In a frame of the hyperbolic theory the status of dynamics observed in these systems is not so well defined because the classic formulation of the theory relates to finite-dimensional syst

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Conclusionthat we have a collection of realistic concrete examples of physically realizable systems with chaotic dynamics, to which the principles of the hyperbolic theory arc applicable (“systems with axiom A”).

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pplications of the mathematical theory."Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attr