Title | Dynamical Systems IX [electronic resource] : Dynamical Systems with Hyperbolic Behaviour / edited by D. V. Anosov |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995 |

Connect to | http://dx.doi.org/10.1007/978-3-662-03172-8 |

Descript | VIII, 236 p. online resource |

SUMMARY

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

CONTENT

1. Hyperbolic Sets -- 2. Strange Attractors -- 3. Cascades on Surfaces -- 4. Dynamical Systems with Transitive Symmetry Group. Geometric and Statistical Properties -- Author Index

Mathematics
Topological groups
Lie groups
Mathematical analysis
Analysis (Mathematics)
Functions of real variables
Differential geometry
Manifolds (Mathematics)
Complex manifolds
Physics
Mathematics
Manifolds and Cell Complexes (incl. Diff.Topology)
Differential Geometry
Analysis
Real Functions
Topological Groups Lie Groups
Mathematical Methods in Physics