Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour: 66 (Encyclopaedia of Mathematical Sciences, 66) - Image 1

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Springer Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour: 66 (Encyclopaedia of Mathematical Sciences, 66)

Name: Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour: 66 (Encyclopaedia of Mathematical Sciences, 66)
Brand: Springer
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This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details). From the Back Cover The book deals with smooth dynamical systems with hyperbolic behaviour of trajectories filling out "large subsets" of the phase space. Such systems lead to complicated motion (so-called "chaos"). The book begins with a discussion of the topological manifestations of uniform and total hyperbolicity: hyperbolic sets, Smale's Axiom A, structurally stable systems, Anosov systems, and hyperbolic attractors of dimension or codimension one. There are various modifications of hyperbolicity and in this connection the properties of Lorenz attractors, pseudo-analytic Thurston diffeomorphisms, and homogeneous flows with expanding and contracting foliations are investigated. These last two questions are discussed in the general context of the theory of homeomorphisms of surfaces and of homogeneous flows.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 3642081681
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Reference
Domain: Amazon UK
Release Date: 05 December 2010
Listed Since: 20 September 2010

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Springer Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour: 66 (Encyclopaedia of Mathematical Sciences, 66)

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