Dynamical systems 02

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it. 1. Ordinary Differential Equations And Smooth Dynamical Systems By D.v. Anosov, V.i. Arnold (eds.). 2. Ergodic Theory With Applications To Dynamical Systems An D Statistical Mechanics By Ya. G. Sinai (ed.). 3. [without Special Title]. 4. S Ymplectic Geometry And Its Applications By V.i. Arnold, S.p. Novikov (eds.). ʹd (ed.) 1. Ordinary Differential Equations And Smooth Dynamical Systems / D.v. Anosov, V.i. Arnold (eds.) -- 2. Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics / Ya. G. Sinai (ed.) -- 3. [without Special Title] -- 4. Symplectic Geometry And Its Applications / V.i. Arnolʹd, S.p. Novikov (eds.)-- 5. Bifurcation Theory And Catastrophe Theory / V.i. Arnolʹd (ed.)-- 6. Singularity Theory I / V.i. Arnolʹd (ed.) -- 8. Singularity Theory Ii Applications / V.i. Arn. D.v. Anosov, V.i. Arnold (ed.). Translation Of: Dinamicheskie Sistemy, Issued As Part Of The Series: Itogi Nauki I Tekhniki. Serii︠a︡ Sovremennye Problemy Matematiki. Vol. 3 Edited By V.i. Arnolʹd; V. 4 By V.i. Arnolʹd, S.p. Novikov. Includes Bibliographies And Index.