Equivalencies between beta-shifts and S-gap shifts

Authors : Dawoud AHMADI DASTJERDI, Somayyeh JANGJOOYE SHALDEHI

Pages : 212-227

Doi:10.3906/mat-1406-32

View : 7 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let Xb be a b -shift for b \in insert ignore into journalissuearticles values(1, 2] and Xinsert ignore into journalissuearticles values(S); a S-gap shift for S\subseteq N \cup {0}. We show that if X\beta is SFT insert ignore into journalissuearticles values(resp. sofic);, then there is a unique S-gap shift conjugate insert ignore into journalissuearticles values(resp. right-resolving almost conjugate); to this X\beta, and if X\beta is not SFT, then no S-gap shift is conjugate to X\beta. For any synchronized Xb , an Xinsert ignore into journalissuearticles values(S); exists such that Xb and Xinsert ignore into journalissuearticles values(S); have a common synchronized 1-1 a.e. extension. For a nonsynchronized X\beta, this common extension is just an almost Markov synchronized system with entropy preserving maps. We then compute the zeta function of Xb from the zeta function of that Xinsert ignore into journalissuearticles values(S);.
Keywords : Shift of finite type, sofic, right resolving, synchronized, finite equivalence, almost conjugacy, zeta function