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.
Hierarchical coding and normal sequences by O. N. Ageev and A. M. Stepin On the number of flattening points on space curves by V. Arnold Invariant tori and symplectic topology by M. Bialy and L. Polterovich On Morse-Smale endomorphisms by M. Brin and Ya. Pesin Continued fractions and geometrical optics by L. A. Bunimovich On statistical properties of chaotic dynamical systems by N. I. Chernov Lyapunov exponents of the Schrodinger equation with certain classes of ergodic potentials by I. Goldsheid and E. Sorets Geometric interpretation of entropy for random processes by B. M. Gurevich A two-dimensional version of the folklore theorem by M. Jakobson and S. Newhouse Thermodynamic formalism for random transformations and statistical mechanics by K. Khanin and Y. Kifer Bounded orbits of nonquasiunipotent flows on homogeneous spaces by D. Y. Kleinbock and G. A. Margulis On solutions of infinite-dimensional systems of ordinary differential equations originating in statistical mechanics by T. V. Lokot and L. D. Pustylnikov Ground states of a boson quantum lattice model by A. E. Mazel and Y. M. Suhov Fast ""turbulent"" dynamo for smooth maps on the two-torus by V. Oseledets Mechanical background of Brownian Motion by M. Soloveitchik.