Shifts of finite type and random substitutions

Gohlke, Philipp; Rust, Dan and Spindeler, Timo (2019). Shifts of finite type and random substitutions. Discrete & Continuous Dynamical Systems - A, 39(9) pp. 5085–5103.

DOI: https://doi.org/10.3934/dcds.2019206

Abstract

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 the logarithm of 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.

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