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WAP Systems and Labeled Subshifts
About this Title
Ethan Akin, Mathematics Department, The City College, 137 Street and Convent Avenue, New York City, New York 10031 and Eli Glasner, Department of Mathematics, Tel-Aviv University, Ramat Aviv, Israel
Publication: Memoirs of the American Mathematical Society
Publication Year:
2019; Volume 262, Number 1265
ISBNs: 978-1-4704-3761-9 (print); 978-1-4704-5503-3 (online)
DOI: https://doi.org/10.1090/memo/1265
Published electronically: December 18, 2019
Keywords: WAP,
HAE,
LE dynamical systems,
space of labels,
expanding functions,
enveloping semigroup,
adherence semigroup,
subshifts,
countable subshifts,
symbolic dynamics,
null,
tame
MSC: Primary 37Bxx, 37B10, 54H20, 54H15
Table of Contents
Chapters
- Introduction
- 1. WAP systems
- 2. Labels and their dynamics
- 3. Labeled subshifts
- 4. WAP labels and their subshifts
- 5. Dynamical properties of $X(\mathcal {M})$
- 6. Scrambled sets
- A. Directed sets and nets
- B. Ellis semigroups and Ellis actions
Abstract
The main object of this work is to present a powerful method of construction of subshifts which we use chiefly to construct WAP systems with various properties. Among many other applications of this so called labeled subshifts, we obtain examples of null as well as non-null WAP subshifts, WAP subshifts of arbitrary countable (Birkhoff) height, and completely scrambled WAP systems of arbitrary countable height. We also construct LE but not HAE subshifts, and recurrent non-tame subshifts- Ethan Akin, The general topology of dynamical systems, Graduate Studies in Mathematics, vol. 1, American Mathematical Society, Providence, RI, 1993. MR 1219737
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