Shifts of finite type and random substitutions

We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substituti...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Gohlke, Philipp, Rust, Dan, Spindeler, Timo
Format: Article
Language:English
Subjects:
Real numbers
Substitutes
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Summary:We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substitution subshifts contains all Perron numbers and so is dense in the positive real numbers. We also provide an independent proof of this density statement using elementary methods.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.05340