Sinai’s Moscow Seminar on Dynamical Systems
About this Title
L. A. Bunimovich, Georgia Institute of Technology, B. M. Gurevich, Moscow State University and Yakov B. Pesin, Pennsylvania State University, Editors. Translated by Moscow group
Publication: American Mathematical Society Translations: Series 2
Publication Year 1996: Volume 171
ISBNs: 978-0-8218-0456-8 (print); 978-1-4704-3382-6 (online)
MathSciNet review: MR1359087
MSC: Primary 00B15; Secondary 28-06, 82C05
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.
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 Morse-Smale endomorphisms
- L. A. Bunimovich – Continued fractions and geometric optics
- N. I. Chernov – On statistical properties of chaotic dynamical systems
- Ilya Goldsheid and Eugene Sorets – Lyapunov exponents of the Schrödinger equation with certain classes of ergodic potentials
- B. M. Gurevich – Geometric interpretation of entropy for random processes
- Michael Jakobson and Sheldon Newhouse – A two-dimensional 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 infinite-dimensional systems of ordinary differential equations originating in statistical mechanics
- Alexander E. Mazel and Yurii M. Suhov – Ground states of a boson quantum lattice model
- V. Oseledets – Fast “turbulent” dynamo for smooth maps on the two-torus
- M. Soloveitchik – Mechanical background of Brownian motion