Topics in Ergodic Theory (PMS-44), Volume 44 /

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

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 som...

Full description

Saved in:
Bibliographic Details
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
Online Access:
Physical Description:1 online resource (226 p.) :; 38 line illus.
Tags: Add Tag
No Tags, Be the first to tag this record!
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

Similar Items