Title: Dynamical Systems IX
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.
Subjects: Mathematics, Cell aggregation, Mathematical physics, Topological Groups, Differentiable dynamical systems, Chaotic behavior in systems, Geometry, non-euclidean, Manifolds and Cell Complexes (incl. Diff.Topology), Real Functions, Lie Groups Topological Groups, Mathematical Methods in Physics, Numerical and Computational Physics