Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Algebraic Ideas in Ergodic Theory
 
Klaus Schmidt Vienna University, Vienna, Austria
A co-publication of the AMS and CBMS
Algebraic Ideas in Ergodic Theory
Softcover ISBN:  978-0-8218-0727-9
Product Code:  CBMS/76
List Price: $47.00
Individual Price: $37.60
eBook ISBN:  978-1-4704-2436-7
Product Code:  CBMS/76.E
List Price: $44.00
Individual Price: $35.20
Softcover ISBN:  978-0-8218-0727-9
eBook: ISBN:  978-1-4704-2436-7
Product Code:  CBMS/76.B
List Price: $91.00 $69.00
Algebraic Ideas in Ergodic Theory
Click above image for expanded view
Algebraic Ideas in Ergodic Theory
Klaus Schmidt Vienna University, Vienna, Austria
A co-publication of the AMS and CBMS
Softcover ISBN:  978-0-8218-0727-9
Product Code:  CBMS/76
List Price: $47.00
Individual Price: $37.60
eBook ISBN:  978-1-4704-2436-7
Product Code:  CBMS/76.E
List Price: $44.00
Individual Price: $35.20
Softcover ISBN:  978-0-8218-0727-9
eBook ISBN:  978-1-4704-2436-7
Product Code:  CBMS/76.B
List Price: $91.00 $69.00
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 761990; 94 pp
    MSC: Primary 28; 54; Secondary 22; 46

    This book is based on a series of ten lectures sponsored by the Conference Board on the Mathematical Sciences and presented by the author at the University of Washington in Seattle in July 1989. The main theme of the lectures, the influence of algebraic ideas on the development of ergodic theory, was so extensive that the author chose to restrict himself to two specific topics.

    The first topic is the influence of operator algebras on dynamics. The author concentrates on ergodic equivalence relations, their properties, and their classification, presenting occasional glimpses of the operator-algebraic context from which many of the ideas and techniques arose. In addition, he provides a large number of examples showing that equivalence relations provide a natural setting for many classical constructions and classification problems.

    The second topic in the book is higher dimensional Markov shifts, a difficult field of research with no indication yet of a satisfactory general theory. After discussing some elementary examples of such shifts and the surprising difficulties these examples present, the author makes the assumption that the Markov shift carries a group structure. In that context, many of the difficulties can be resolved, and one has the beginnings of a successful analysis which exhibits an intriguing interplay between commutative algebra and dynamics.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 1. Operator Algebras and Dynamical Systems
    • 2. Cohomology of Equivalence Relations
    • 3. Rokhlin’s Lemma and Asymptotic Invariance
    • 4. Dimension
    • 5. Markov Shifts in Higher Dimensions
    • 6. Markov Shifts and Markov Groups
    • 7. The Dynamics of Abelian Markov Groups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 761990; 94 pp
MSC: Primary 28; 54; Secondary 22; 46

This book is based on a series of ten lectures sponsored by the Conference Board on the Mathematical Sciences and presented by the author at the University of Washington in Seattle in July 1989. The main theme of the lectures, the influence of algebraic ideas on the development of ergodic theory, was so extensive that the author chose to restrict himself to two specific topics.

The first topic is the influence of operator algebras on dynamics. The author concentrates on ergodic equivalence relations, their properties, and their classification, presenting occasional glimpses of the operator-algebraic context from which many of the ideas and techniques arose. In addition, he provides a large number of examples showing that equivalence relations provide a natural setting for many classical constructions and classification problems.

The second topic in the book is higher dimensional Markov shifts, a difficult field of research with no indication yet of a satisfactory general theory. After discussing some elementary examples of such shifts and the surprising difficulties these examples present, the author makes the assumption that the Markov shift carries a group structure. In that context, many of the difficulties can be resolved, and one has the beginnings of a successful analysis which exhibits an intriguing interplay between commutative algebra and dynamics.

  • Chapters
  • 1. Introduction
  • 1. Operator Algebras and Dynamical Systems
  • 2. Cohomology of Equivalence Relations
  • 3. Rokhlin’s Lemma and Asymptotic Invariance
  • 4. Dimension
  • 5. Markov Shifts in Higher Dimensions
  • 6. Markov Shifts and Markov Groups
  • 7. The Dynamics of Abelian Markov Groups
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.