Dynamical Systems IX
Dynamical Systems with Hyperbolic Behaviour
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Beschreibung
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.
The book is a comprehensive survey of one of the most attractive fields of research in mathematics, namely the theory of hyperbolic dynamical systems. This subject forms the theoretical basis for what is sometimes called the "theory of chaos". The book addresses graduate students and researchers in mathematics and physics.
Autor*in
D.V. Anosov
Themen in »Dynamical Systems IX«
Ergodic flow Ergodischer Fluß Isotopieklasse Symmetry group diffeomorphism homogener Fluß homogenous flow hyperbolic set hyperbolische Menge isotopy class seltsame Attraktor strange attractor