American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1996; 247 pp; hardcover Volume: 171 ISBN10: 0821804561 ISBN13: 9780821804568 List Price: US$116 Member Price: US$92.80 Order Code: TRANS2/171
 This book is a collection of papers written by participants in the seminar of Ya. G. Sinai, which has for thirty years played the leading role in shaping the modern statistical and topological theory of dynamical systems. The seminar has served as the major place for new ideas and approaches in the ergodic theory of dynamical systems. These papers, written by internationally known mathematicians, represent the major part of the enormous variety of Sinai's scientific interests. The following topics are discussed: hyperbolic dynamical systems, limit theorems for dynamical systems with chaotic behavior, thermodynamic formalism, symbolic dynamics, symplectic geometry, statistical mechanics, and more. The book reflects the unique style of Sinai's school and its interest in various interconnections between ergodic theory and various other branches of mathematics and physics. Readership Graduate students and research mathematicians working in dynamical systems, ergodic theory, and statistical mechanics. Table of Contents  O. N. Ageev and A. M. Stepin  Hierarchical coding and normal sequences
 V. Arnold  On the number of flattening points on space curves
 M. Bialy and L. Polterovich  Invariant tori and symplectic topology
 M. Brin and Ya. Pesin  On MorseSmale endomorphisms
 L. A. Bunimovich  Continued fractions and geometrical optics
 N. I. Chernov  On statistical properties of chaotic dynamical systems
 I. Goldsheid and E. Sorets  Lyapunov exponents of the Schrödinger equation with certain classes of ergodic potentials
 B. M. Gurevich  Geometric interpretation of entropy for random processes
 M. Jakobson and S. Newhouse  A twodimensional version of the folklore theorem
 K. Khanin and Y. Kifer  Thermodynamic formalism for random transformations and statistical mechanics
 D. Y. Kleinbock and G. A. Margulis  Bounded orbits of nonquasiunipotent flows on homogeneous spaces
 T. V. Lokot' and L. D. Pustyl'nikov  On solutions of infinitedimensional systems of ordinary differential equations originating in statistical mechanics
 A. E. Mazel and Y. M. Suhov  Ground states of a boson quantum lattice model
 V. Oseledets  Fast "turbulent" dynamo for smooth maps on the twotorus
 M. Soloveitchik  Mechanical background of Brownian Motion
