Dynamical Systems IX: Dynamical Systems With Hyperbolic Behaviour: 66 - Hardcover
Book 15 of 47: Encyclopaedia of Mathematical Sciences
Synopsis
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.
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Dynamical Systems IX: Dynamical Systems With Hyperbolic Behaviour, Hardcover edition
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Secaucus, New Jersey, U.S.A.: Springer Verlag, 1995
ISBN 10: 0387570438
ISBN 13: 9780387570433
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