TY - BOOK ID - 65509333 TI - Profinite semigroups and symbolic dynamics PY - 2020 SN - 3030552152 3030552144 PB - Cham, Switzerland : Springer, DB - UniCat KW - Group theory. KW - Computer science—Mathematics. KW - Dynamics. KW - Ergodic theory. KW - Mathematical logic. KW - Group Theory and Generalizations. KW - Discrete Mathematics in Computer Science. KW - Dynamical Systems and Ergodic Theory. KW - Mathematical Logic and Formal Languages. KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Mathematics KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Profinite groups. KW - Group theory UR - https://www.unicat.be/uniCat?func=search&query=sysid:65509333 AB - 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. ER -