Hardcover ISBN:  9780821804568 
Product Code:  TRANS2/171 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470433826 
Product Code:  TRANS2/171.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821804568 
eBook: ISBN:  9781470433826 
Product Code:  TRANS2/171.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 
Hardcover ISBN:  9780821804568 
Product Code:  TRANS2/171 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470433826 
Product Code:  TRANS2/171.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821804568 
eBook ISBN:  9781470433826 
Product Code:  TRANS2/171.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 171; 1996; 247 ppMSC: Primary 28; 58
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.
ReadershipGraduate students and research mathematicians working in dynamical systems, ergodic theory, and statistical mechanics.

Table of Contents

Chapters

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 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 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

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 twotorus

M. Soloveitchik — Mechanical background of Brownian motion


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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.

Chapters

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 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 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

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 twotorus

M. Soloveitchik — Mechanical background of Brownian motion