Synopses & Reviews
This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.
"... The list of topics gives some idea of the impressive scope of this volume, and the comprehensive bibliographies represent the state of knowledge right up to the late 1990's. ... This survey is much more than a place where one can quickly look up the current state of knowledge on a particular topic or get an idea about the scope of a branch of the theroy. It is also highly recommended and fascinating reading for experts in the subject: the individual chapters are written by top experts inthe field, whose insights and illuminating remarks will reward readers at any level of expertise. The coverage of both 'mathematical' and 'physical' aspects of the theory in a single volume and from a reasonably unified point of view is another very attractive and quite unique feature of this volume." K.Schmidt, Wien, Monathshefte für Mathematik, Vol. 139, Issue 4, p.351, 2003 "... This Encyclopaedia volume is indeed (as the publisher writes on the back-cover of the book) compulsory reading for all mathematicians working in this field, or wanting to learn about it." W.T.van Horssen, ZAMM 82 (2002), Issue 8
Includes bibliographical references and index.
Table of Contents
I. General Ergodic Theory of Groups of Measure Preserving Transformations (contributions by I.P.Kornfeld, Ya.G.Sinai, and A.M.Vershik).- II. Ergodic Theory of Smooth Dynamical Systems (contributions by L.A.Bunimovich, M.V.Jakobson, Y.B.Pesin, and Ya.G.Sinai).- III. Dynamical Systems on Homogeneous Spaces (by S.G.Dani).- IV. The Dynamics of Billiard Flows in Rational Polygons (by J.Smillie).- V. Dynamical Systems of Statistical Mechanics and Kinetic Equations (contributions by R.L.Dobrushin, N.B.Maslova, Ya.G.Sinai, and Yu.M.Sukhov).- References.- Subject Index