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Mathematics - Analysis | Dynamical Systems, Ergodic Theory and Applications

Dynamical Systems, Ergodic Theory and Applications

Bunimovich, L.A., Dani, S.G., Dobrushin, R.L., Jakobson, M.V., Kornfeld, I.P., Maslova, N.B., Pesin, Y.B., Sinai, Y.G., Smillie, J., Sukhov, Y.M., Vershik, A.M.

Sinai, Ya.G. (Ed.)

Originally published as volume 2 in the series: Encyclopaedia of Mathematical Sciences with the title: Dynamical Systems II

2nd exp. and rev. ed. 2000, XI, 460 p.

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This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Content Level » Research

Keywords » dynamical systems - ergodic theorem - hyperbolicity - invariant measure - spectrum of dynamical systems

Related subjects » Analysis - Complexity - Geometry & Topology

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