By Sergey P. Kuznetsov
"Hyperbolic Chaos: A Physicist’s View” offers contemporary development on uniformly hyperbolic attractors in dynamical structures from a actual instead of mathematical point of view (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally good attractors take place powerful stochastic houses, yet are insensitive to edition of capabilities and parameters within the dynamical structures. according to those features of hyperbolic chaos, this monograph exhibits how to define hyperbolic chaotic attractors in actual structures and the way to layout a actual platforms that own hyperbolic chaos.
This ebook is designed as a reference paintings for college professors and researchers within the fields of physics, mechanics, and engineering.
Dr. Sergey P. Kuznetsov is a professor on the division of Nonlinear methods, Saratov kingdom collage, Russia.
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Further, each basic set can be decomposed to a union of a finite number k i 1 of disjoint subsets Xi, j , visited in a certain fixed order under iteration of the map. Each set X i, j is an invariant set for the map iterated ki times. , they do not allow further decomposition). Unless otherwise is not indicated specially (Part III of the present book), we will have in mind only attractors, whose unstable manifolds are one-dimensional. 5 One particular class of systems with axiom A is represented by Anosov systems, like the Arnold cat map; their specificity is that for them the set of non-wandering points is the whole phase space.
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1995; Katok and Hasselblatt, 1995; Shilnikov, 1997; Guckenheimer and Holmes, 1983; Afraimovich and Hsu, 2003; Devaney, 2003; Hasselblatt and Young, 2005). Ergodicity means that a typical trajectory on the attractor visits during the time evolution any neighborhood of any point on the attractor. It corresponds to equivalence of averaging over time and averaging over invariant measure and provides a statistical approach to the analysis of sustained regimes of dynamics. The mixing property is stronger.