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OverviewThis 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. Full Product DetailsAuthor: Jorge Almeida , Alfredo Costa , Revekka Kyriakoglou , Dominique PerrinPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2020 Volume: 2274 Weight: 0.454kg ISBN: 9783030552145ISBN 10: 3030552144 Pages: 278 Publication Date: 10 September 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents- Introduction. - Prelude: Profinite Integers. - Profinite Groups and Semigroups. - Free Profinite Monoids, Semigroups and Groups. - Shift Spaces. - Sturmian Sets and Tree Sets. - The Schützenberger Group of a Minimal Set. - Groups of Bifix Codes.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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