An Introduction to Infinite Ergodic Theory

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American Mathematical Soc., 1997 - Mathematics - 284 pages
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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.
 

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Contents

General ergodic and spectral theorems
53
Transformations with infinite invariant measures
85
Markov maps
139
Recurrent events and similarity of Markov shifts
181
Inner functions
201
Hyperbolic geodesic flows
223
Cocycles and skew products
247
Bibliography
275
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