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Dynamical Systems IX

Dynamical Systems with Hyperbolic Behaviour

  • D. V. Anosov
Book

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 66)

Table of contents

  1. Front Matter
    Pages I-9
  2. D. V. Anosov, V. V. Solodov
    Pages 10-92
  3. R. V. Plykin, E. A. Sataev, S. V. Shlyachkov
    Pages 93-139
  4. S. Kh. Aranson, V. Z. Grines
    Pages 141-175
  5. A. V. Safonov, A. N. Starkov, A. M. Stepin
    Pages 177-230
  6. Back Matter
    Pages 231-238

About this book

Introduction

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.

Keywords

Ergodic flow Ergodischer Fluß Isotopieklasse Symmetry group diffeomorphism homogener Fluß homogenous flow hyperbolic set hyperbolische Menge isotopy class seltsame Attraktor strange attractor

Editors and affiliations

  • D. V. Anosov
    • 1
  1. 1.Steklov Mathematical InstituteMoscow GSP-1Russia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03172-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08168-2
  • Online ISBN 978-3-662-03172-8
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site