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Weakly Wandering Sequences in Ergodic Theory de Stanley Eigen

Weakly Wandering Sequences in Ergodic Theory: Springer Monographs in Mathematics

Autor Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
en Limba Engleză Paperback – 23 aug 2016
The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.
This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.
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Specificații

ISBN-13: 9784431564003
ISBN-10: 4431564004
Pagini: 167
Ilustrații: XIV, 153 p. 15 illus.
Dimensiuni: 155 x 235 x 9 mm
Greutate: 0.25 kg
Ediția:Softcover reprint of the original 1st ed. 2014
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării:Tokyo, Japan

Cuprins

1. Existence of a finite invariant measure 2. Transformations with no Finite Invariant Measure 3. Infinite Ergodic Transformations 4. Three Basic Examples 5. Properties of Various Sequences 6. Isomorphism Invariants 7. Integer Tilings

Recenzii

“This is a well-written book that should be the place to go to for someone interested in weakly wandering sequences, their properties and extensions. Most of the work the authors discuss is the result of their research over a number of years. At the same time we would have liked to see discussions of several topics that are connected to the topics of the book, such as inducing, rank-one transformations, and Maharam transformations.” (Cesar E. Silva, Mathematical Reviews, May, 2016)
“The subject of the book under review is ergodic theory with a stress on WW sequences. … The book is interesting, well written and contains a lot of examples. It constitutes a valuable addition to the mathematical pedagogical literature.” (Athanase Papadopoulos, zbMATH, 1328.37006, 2016)

Notă biografică

Arshag Hajian Professor of Mathematics at Northeastern University, Boston, Massachusetts, U.S.A. Stanley Eigen Professor of Mathematics at Northeastern University, Boston, Massachusetts, U. S. A. Raj. Prasad Professor of Mathematics at University of Massachusetts at Lowell, Lowell, Massachusetts, U.S.A. Yuji Ito Professor Emeritus of Keio University, Yokohama, Japan.

Textul de pe ultima copertă

The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.
This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.

Caracteristici

Provides a full account of the problem of finite invariant measures for measurable transformations with a detailed explanation of its history Explains in detail the properties and significance of weakly wandering and other sequences of integers attached to infinite ergodic transformations Shows interesting new connections between ergodic theory and certain number theoretic problems