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

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface vii
4. Part I. General Ergodic Theory
5. Lecture 1. Measurable Transformations. Invariant Measures. Ergodic Theorems 1
6. Lecture 2. Lebesgue Spaces and Measurable Partitions. Ergodicity and Decomposition into Ergodic Components. Spectrum of Interval Exchange Transformations 16
7. Lecture 3. Isomorphism of Dynamical Systems. Generators of Dynamical Systems 28
8. Lecture 4. Dynamical Systems with Pure Point Spectra 36
9. Lecture 5. General Properties of Eigenfunctions and Eigenvalues of Ergodic Automorphisms. Isomorphism of Dynamical Systems with Pure Point Spectrum 43
10. Part II. Entropy Theory of Dynamical Systems
11. Lecture 6. Entropy Theory of Dynamical Systems 53
12. Lecture 7. Breiman Theorem. Pinsker Partition. K-Systems. Exact Endomorphisms. Gibbs Measures 69
13. Lecture 8. Entropy of Dynamical Systems with Multidimensional Time. Systems of Cellular Automata as Dynamical Systems 77
14. Part III. One-Dimensional Dynamics
15. Lecture 9. Continued Fractions and Farey Fractions 85
16. Lecture 10. Homeomorphisms and Diffeomorphisms of the Circle 95
17. Lecture 11. Sharkovski's Ordering and Feigenbaum's Universality 111
18. Lecture 12. Expanding Mappings of the Circle 123
19. Part IV. Two-Dimensional Dynamics
20. Lecture 13. Standard Map. Twist Maps. Periodic Orbits. Aubry-Mather Theory 135
21. Lecture 14. Periodic Hyperbolic Points, Their Stable and Unstable Manifolds. Homoclinic and Heteroclinic Orbits 147
22. Lecture 15. Homoclinic and Heteroclinic Points and Stochastic Layers 167
23. Part V. Elements of the Theory of Hyperbolic Dynamical Systems
24. Lecture 16. Geodesic Flows and Their Generalizations. Discontinuous Dynamical Systems. Stable and Unstable Manifolds 175
25. Lecture 17. Existence of Local Manifolds. Gibbs Measures 194
26. Lecture 18. Markov Partitions. H-Theorem for Dynamical Systems. Elements of Thermodynamic Formalism 204
27. Index 217