Weakly Wandering Sequences in Ergodic Theory

2014
ISBN: 978-4-431-55107-2
Verlag: Springer Japan

Buch, Englisch, 153 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 424 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Eigen, Stanley

Prasad, Vidhu

Hajian, Arshag

Ito, Yuji

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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

Über Autor(innen)

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.