ENGLISH

Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour

By D. V. Anosov , V. V. Solodov (auth.) , D. V. Anosov (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1995
ISBN
978-3-642-08168-2, 978-3-662-03172-8
DOI
10.1007/978-3-662-03172-8
Language
english
Format
PDF
Filesize
7 MB (7581569 bytes)
Series
Encyclopaedia of Mathematical Sciences 66
Edition
1
Pages
236\241
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Lie Groups;Mathematical Methods in Physics;NumericManifolds and Cell Complexes (incl. Diff.Topology)

Description

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.

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