Topics in Ergodic Theory (PMS-44), Volume 44 / Iakov Grigorevich Sinai.

Format:

Book

Author/Creator:

Sinai, Iakov Grigorevich, author.

Series:

Princeton mathematical series ; 44.

Princeton Mathematical Series ; 44

Language:

English

Subjects (All):

Ergodic theory.

Topological dynamics.

Physical Description:

1 online resource (227 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2017]

Language Note:

In English.

Summary:

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems.Originally published in 1993.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Contents:

Frontmatter

Contents

Preface

Part I. General Ergodic Theory

Lecture 1. Measurable Transformations. Invariant Measures. Ergodic Theorems

Lecture 2. Lebesgue Spaces and Measurable Partitions. Ergodicity and Decomposition into Ergodic Components. Spectrum of Interval Exchange Transformations

Lecture 3. Isomorphism of Dynamical Systems. Generators of Dynamical Systems

Lecture 4. Dynamical Systems with Pure Point Spectra

Lecture 5. General Properties of Eigenfunctions and Eigenvalues of Ergodic Automorphisms. Isomorphism of Dynamical Systems with Pure Point Spectrum

Part II. Entropy Theory of Dynamical Systems

Lecture 6. Entropy Theory of Dynamical Systems

Lecture 7. Breiman Theorem. Pinsker Partition. K-Systems. Exact Endomorphisms. Gibbs Measures

Lecture 8. Entropy of Dynamical Systems with Multidimensional Time. Systems of Cellular Automata as Dynamical Systems

Part III. One-Dimensional Dynamics

Lecture 9. Continued Fractions and Farey Fractions

Lecture 10. Homeomorphisms and Diffeomorphisms of the Circle

Lecture 11. Sharkovski's Ordering and Feigenbaum's Universality

Lecture 12. Expanding Mappings of the Circle

Part IV. Two-Dimensional Dynamics

Lecture 13. Standard Map. Twist Maps. Periodic Orbits. Aubry-Mather Theory

Lecture 14. Periodic Hyperbolic Points, Their Stable and Unstable Manifolds. Homoclinic and Heteroclinic Orbits

Lecture 15. Homoclinic and Heteroclinic Points and Stochastic Layers

Part V. Elements of the Theory of Hyperbolic Dynamical Systems

Lecture 16. Geodesic Flows and Their Generalizations. Discontinuous Dynamical Systems. Stable and Unstable Manifolds

Lecture 17. Existence of Local Manifolds. Gibbs Measures

Lecture 18. Markov Partitions. H-Theorem for Dynamical Systems. Elements of Thermodynamic Formalism

Index

Notes:

Includes index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9780691654980

0691654980

9780691628318

0691628319

OCLC:

1004883575