Hardcover ISBN:  9780821804568 
Product Code:  TRANS2/171 
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Electronic ISBN:  9781470433826 
Product Code:  TRANS2/171.E 
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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

Cover

Frontispiece

Title page

Copyright page

Contents

Foreword

Hierarchical coding and normal sequences

On the number of flattening points on space curves

Invariant tori and symplectic topology

On MorseSmale endomorphisms

Continued fractions and geometric optics

On statistical properties of chaotic dynamical systems

Lyapunov exponents of the Schrödinger equation with certain classes of ergodic potentials

Geometric interpretation of entropy for random processes

A twodimensional version of the folklore theorem

Thermodynamic formalism for random transformations and statistical mechanics

Bounded orbits of nonquasiunipotent flows on homogeneous spaces

On solutions of infinitedimensional systems of ordinary differential equations originating in statistical mechanics

Ground states of a boson quantum lattice model

Fast “turbulent” dynamo for smooth maps on the twotorus

Mechanical background of Brownian motion

Back Cover


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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.

Cover

Frontispiece

Title page

Copyright page

Contents

Foreword

Hierarchical coding and normal sequences

On the number of flattening points on space curves

Invariant tori and symplectic topology

On MorseSmale endomorphisms

Continued fractions and geometric optics

On statistical properties of chaotic dynamical systems

Lyapunov exponents of the Schrödinger equation with certain classes of ergodic potentials

Geometric interpretation of entropy for random processes

A twodimensional version of the folklore theorem

Thermodynamic formalism for random transformations and statistical mechanics

Bounded orbits of nonquasiunipotent flows on homogeneous spaces

On solutions of infinitedimensional systems of ordinary differential equations originating in statistical mechanics

Ground states of a boson quantum lattice model

Fast “turbulent” dynamo for smooth maps on the twotorus

Mechanical background of Brownian motion

Back Cover