<p>"The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ...indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." (Journal de Physique)</p>

Dynamical Systems I (ENCYCLOPAEDIA OF MATHEMATICAL SCIENCES)

Science & Math

Vladimir I. Arnold

D.V. Anosov

Samuel Kh. Aranson

I.U. Bronstein

V.Z. Grines

Mathematics

Springer, Verlag

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.

Dynamical Systems IX: Dynamical Systems With Hyperbolic Behaviour

R.V. Plykin

A.V. Safonov

E. A. Sataev

S.V. Shlyachkov

V.V. Solodov

A.N. Starkov

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Books by Samuel Kh. Aranson