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Weakly Wandering Sequences in Ergodic Theory

Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad (Autoren)

Buch | Hardcover

153 Seiten

2014 | 2014 ed.
Springer Verlag, Japan
978-4-431-55107-2 (ISBN)

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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.

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.

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.

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

Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	15 Illustrations, black and white
Verlagsort	Tokyo
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Direct sum decompositions of N and Z • Infinite ergodic transformations • Invariant measures for ergodic transformations • Recurrent and dissipative sequences • Weakly wandering and exhaustive weakly wandering sequences
ISBN-10	4-431-55107-7 / 4431551077
ISBN-13	978-4-431-55107-2 / 9784431551072
Zustand	Neuware