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arXiv · 1708.08511

S-limited shifts

Benjamin Matson·Elizabeth Sattler
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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.

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Benjamin Matson, Elizabeth Sattler. 2017-08-28. S-limited shifts. https://arxiv.org/abs/1708.08511

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