Hardcover ISBN:  9780821804940 
Product Code:  SURV/50 
List Price:  $108.00 
MAA Member Price:  $97.20 
AMS Member Price:  $86.40 
Electronic ISBN:  9781470412814 
Product Code:  SURV/50.E 
List Price:  $101.00 
MAA Member Price:  $90.90 
AMS Member Price:  $80.80 

Book DetailsMathematical Surveys and MonographsVolume: 50; 1997; 284 ppMSC: Primary 28; Secondary 30; 58; 60;
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations.
The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible “ergodic behavior” is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.ReadershipGraduate students and research mathematicians interested in ergodic theory, dynamical systems and/or probability.

Table of Contents

Chapters

1. Nonsingular transformations

2. General ergodic and spectral theorems

3. Transformations with infinite invariant measures

4. Markov maps

5. Recurrent events and similarity of Markov shifts

6. Inner functions

7. Hyperbolic geodesic flows

8. Cocycles and skew products


Reviews

This book is a research monograph and contains an impressive amount of material. The presentation is careful, well organized, and reliable. This monograph is definitely a valuable complement to the ergodic theory literature. It will be useful to graduate students and researchers in ergodic theory and related fields.
Bulletin of the London Mathematical Society 
Accessible to readers with a firm background in measuretheoretic probability … carefully organized and well written … invaluable both as an introduction and as a reference work on its subject, and this definitely is not just because it is the only one at the moment.
Zentralblatt MATH 
This book is devoted mainly to the ergodic theory of transformations preserving an infinite measure, and as such it is a welcome addition to the literature. [O]verall this book fills important gaps in the literature and is recommended to researchers and advanced students.
Mathematical Reviews


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Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations.
The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible “ergodic behavior” is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
Graduate students and research mathematicians interested in ergodic theory, dynamical systems and/or probability.

Chapters

1. Nonsingular transformations

2. General ergodic and spectral theorems

3. Transformations with infinite invariant measures

4. Markov maps

5. Recurrent events and similarity of Markov shifts

6. Inner functions

7. Hyperbolic geodesic flows

8. Cocycles and skew products

This book is a research monograph and contains an impressive amount of material. The presentation is careful, well organized, and reliable. This monograph is definitely a valuable complement to the ergodic theory literature. It will be useful to graduate students and researchers in ergodic theory and related fields.
Bulletin of the London Mathematical Society 
Accessible to readers with a firm background in measuretheoretic probability … carefully organized and well written … invaluable both as an introduction and as a reference work on its subject, and this definitely is not just because it is the only one at the moment.
Zentralblatt MATH 
This book is devoted mainly to the ergodic theory of transformations preserving an infinite measure, and as such it is a welcome addition to the literature. [O]verall this book fills important gaps in the literature and is recommended to researchers and advanced students.
Mathematical Reviews