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Lecture Notes in Mathematics

Profinite Semigroups and Symbolic Dynamics

Authors: Almeida, J., Costa, A., Kyriakoglou, R., Perrin, D.

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  • The first book to describe the relation between profinite semigroups and symbolic dynamics
  • Provides new insights into both fields of profinite semigroups and symbolic dynamics
  • Defines all concepts in detail and provides numerous exercises
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  • ISBN 978-3-030-55215-2
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About this book

This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them.  The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.

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Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-030-55215-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Profinite Semigroups and Symbolic Dynamics
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2274
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-55215-2
DOI
10.1007/978-3-030-55215-2
Softcover ISBN
978-3-030-55214-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 278
Number of Illustrations
63 b/w illustrations, 4 illustrations in colour
Topics

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