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

• Superior document: Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
• VerfasserIn: Sinai, Iakov Grigorevich,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2017]; ©1993
• Year of Publication: 2017
• Language: English
• Series: Princeton Mathematical Series ; 5185
• Physical Description: 1 online resource (226 p.) :; 38 line illus.

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.

Table of 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