## Real Analysis Exchange

### S-Limited Shifts

#### Abstract

In this paper, we explore the construction and dynamical properties of $\mathcal{S}$-limited shifts. An $S$-limited shift is a subshift defined on a finite alphabet $\mathcal{A} = \{1, \ldots,p\}$ by a set $\mathcal{S} = \{S_1, \ldots, S_p\}$, where $S_i \subseteq \mathbb{N}$ describes the allowable lengths of blocks in which the corresponding letter may appear. We give conditions for which an $\mathcal{S}$-limited shift is a subshift of finite type or sofic. We give an exact formula for finding the entropy of such a shift and show that an $\mathcal{S}$-limited shift and its factors must be intrinsically ergodic. Finally, we give some conditions for which two such shifts can be conjugate, and additional information about conjugate $\mathcal{S}$-limited shifts.

#### Article information

Source
Real Anal. Exchange, Volume 43, Number 2 (2018), 393-416.

Dates
First available in Project Euclid: 27 June 2018

https://projecteuclid.org/euclid.rae/1530064969

Digital Object Identifier
doi:10.14321/realanalexch.43.2.0393

Mathematical Reviews number (MathSciNet)
MR3942586

Zentralblatt MATH identifier
06924897

Subjects

Keywords
shift space S-gap shift entropy

#### Citation

Matson, Benjamin; Sattler, Elizabeth. S-Limited Shifts. Real Anal. Exchange 43 (2018), no. 2, 393--416. doi:10.14321/realanalexch.43.2.0393. https://projecteuclid.org/euclid.rae/1530064969