Encyclopaedia of Mathematical Sciences

2 primary works

Dynamical Systems, Ergodic Theory and Applications

by L.A. Bunimovich, S.G. Dani, R. L. Dobrushin, M.V. Jakobson, I P Kornfel'd, N.B. Maslova, Ya B. Pesin, Ya G Sinai, J. Smillie, and Yu.M. Sukhov

Published 3 December 2010

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.

Hard Ball Systems and the Lorentz Gas

by L.A. Bunimovich, D. Burago, N. Chernov, E.G.D. Cohen, C.P. Dettmann, J. R. Dorfman, S. Ferleger, R. Hirschl, and A. Kononenko

Published 4 December 2000

Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.