Ergodic theory with applications to dynamical systems and statistical mechanics
著者
書誌事項
Ergodic theory with applications to dynamical systems and statistical mechanics
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 2 . Dynamical systems ; 2）
Springer-Verlag, c1989
- : gw
- : us
- タイトル別名
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Dinamicheskie sistemy
Itogi nauki i tekhniki. Serii︠a︡ Sovremennye problemy matematiki
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注記
"Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, Vol. 2, Dinamicheskie sistemy 2, publisher VINITI, Moscow 1985"--T.p. verso
Includes bibliographies and index
内容説明・目次
内容説明
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.
目次
Contents: Basic Notions of Ergodic Theory and Examples of Dynamical Systems.- Spectral Theory of Dynamical Systems.- Entropy Theory of Dynamical Systems.- Periodic Approximations and Their Applications. Ergodic Theorems, Spectral and Entropy Theory for the General Group Actions.- Trajectory Theory.- Bibliography.
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