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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-calledchaos). The book begins with a discussion of the topological manifestations of uniform and total hyperbolicity: hyperbolic sets, Smales 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.
目次
Preface
Chapter 1. Hyperbolic Sets
Chapter 2. Strange Attractors
Chapter 3. Cascades on Surfaces
Chapter 4. Dynamical Systems with Transitive Symmetry Group. Geometric and Statistical Properties
Author Index
Subject Index
Chapter 1. Hyperbolic Sets
Chapter 2. Strange Attractors
Chapter 3. Cascades on Surfaces
Chapter 4. Dynamical Systems with Transitive Symmetry Group. Geometric and Statistical Properties
Author Index
Subject Index
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