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



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