American Institute of Mathematical Sciences

September  2019, 39(9): 5085-5103. doi: 10.3934/dcds.2019206

Shifts of finite type and random substitutions

 1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany 2 Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, AB, T6G 2G1, Canada

Received  May 2018 Revised  January 2019 Published  May 2019

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.

Citation: Philipp Gohlke, Dan Rust, Timo Spindeler. Shifts of finite type and random substitutions. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 5085-5103. doi: 10.3934/dcds.2019206
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References:
Graph $G_{A}$ of the SFT $X_{A}$ in Example 5.8
Graph $G$ with labelled edges for Example 5.11
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