Weakly wandering sequences in ergodic theory / Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad.

Format:

Book

Author/Creator:

Eigen, Stanley, author.

Hajian, Arshag, author.

Itō, Yūji, 1935- author.

Prasad, Vidhu, author.

Contributor:

Kakutani, Shizuo, 1911-2004, dedicatee.

Series:

Springer monographs in mathematics

Language:

English

Subjects (All):

Ergodic theory.

Physical Description:

xiv, 153 pages : illustration ; 24 cm.

Place of Publication:

Tokyo ; New York : Springer, [2014]

Summary:

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.

Contents:

1. Existence of 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.

Notes:

Includes bibliographical references and index.

"This monograph is dedicated to Professor Shizuo Kakutani, 1911-2004."

ISBN:

4431551077

9784431551072

OCLC:

881309335