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arXiv · 1207.0091

Equivalencies between beta-shifts and S-gap shifts

D. Ahmadi Dastjerdi·S. Jangjooye Shaldehi
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Abstract

Let $ X_β$ be a sofic $ β$-shift for $ β\in (1, 2] $. We show that there is an $ S $-gap shift $ X(S) $ such that $ X_β $ and $ X(S) $ are right-resolving almost conjugate. Conversely, a condition on $ S \subseteq \mathbb N\cup \{0\} $ is given such that for this $S$, there is a $ β$ such that $ X(S) $ and $ X_β $ have the same equivalency. We show that if $X_β$ is SFT, then there is an $S$-gap shift conjugate to this $X_β$; however, if $X_β$ is not SFT, then no $S$-gap shift is conjugate to $X_β$. Also we will investigate the existence of these sort of equivalencies for non-sofics.

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D. Ahmadi Dastjerdi, S. Jangjooye Shaldehi. 2012-06-30. Equivalencies between beta-shifts and S-gap shifts. https://arxiv.org/abs/1207.0091

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