02304nam 2200445 450 99641825790331620210226090905.03-030-55215-210.1007/978-3-030-55215-2(CKB)4100000011435812(DE-He213)978-3-030-55215-2(MiAaPQ)EBC6348314(PPN)250220490(EXLCZ)99410000001143581220210226d2020 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierProfinite semigroups and symbolic dynamics /Jorge Almeida [and three others]1st ed. 2020.Cham, Switzerland :Springer,[2020]©20201 online resource (IX, 278 p. 67 illus., 4 illus. in color.) Lecture notes in mathematics (Springer-Verlag) ;22743-030-55214-4 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.Lecture notes in mathematics (Springer-Verlag) ;2274.Profinite groupsProfinite groups.512.2Almeida Jorge1005289MiAaPQMiAaPQMiAaPQBOOK996418257903316Profinite semigroups and symbolic dynamics2311010UNISA