Topics in Ergodic Theory [online] / Iakov Grigorevich Sinai

vol. 44 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

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