Dynamical Systems IX
Dynamical Systems with Hyperbolic Behaviour
Editors: Anosov, D.V. (Ed.)
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- About this book
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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-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.
- Table of contents (4 chapters)
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Hyperbolic Sets
Pages 10-92
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Strange Attractors
Pages 93-139
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Cascades on Surfaces
Pages 141-175
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Dynamical Systems with Transitive Symmetry Group. Geometric and Statistical Properties
Pages 177-230
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Table of contents (4 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Dynamical Systems IX
- Book Subtitle
- Dynamical Systems with Hyperbolic Behaviour
- Editors
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- D.V. Anosov
- Translated by
- Gould, G.G.
- Series Title
- Encyclopaedia of Mathematical Sciences
- Series Volume
- 66
- Copyright
- 1995
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-662-03172-8
- DOI
- 10.1007/978-3-662-03172-8
- Hardcover ISBN
- 978-3-540-57043-1
- Softcover ISBN
- 978-3-642-08168-2
- Series ISSN
- 0938-0396
- Edition Number
- 1
- Number of Pages
- VIII, 236
- Additional Information
- Original Russian edition published by VINITI, Moscow, 1991
- Topics
