Real Analysis Exchange

S-Limited Shifts

Benjamin Matson and Elizabeth Sattler

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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

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

First available in Project Euclid: 27 June 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx]

shift space S-gap shift entropy


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

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