Turkish Journal of Mathematics
Abstract
Let X_{\beta} be a \beta -shift for \beta \in (1, 2] and X(S) a S-gap shift for S\subseteq N \cup {0}. We show that if X_\beta is SFT (resp. sofic), then there is a unique S-gap shift conjugate (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 X_{\beta} , an X(S) exists such that X_{\beta} and X(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 X_{\beta} from the zeta function of that X(S).
DOI
10.3906/mat-1406-32
Keywords
Shift of finite type, sofic, right-resolving, synchronized, finite equivalence, almost conjugacy, zeta function
First Page
212
Last Page
227
Recommended Citation
DASTJERDI, DAWOUD AHMADI and SHALDEHI, SOMAYYEH JANGJOO
(2015)
"Equivalencies between beta-shifts and S-gap shifts,"
Turkish Journal of Mathematics: Vol. 39:
No.
2, Article 6.
https://doi.org/10.3906/mat-1406-32
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss2/6
