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Mixing properties and entropy bounds of a family of Pisot random substitutions

2021/03/08 by Giovanni B. Escolano, Escolano, Giovanni B., Neil Mañibo +3
Computer Science · Mathematics · Biochemistry, Genetics and Molecular Biology · #semigroups and automata theory #Mathematical Dynamics and Fractals #Biochemical and Structural Characterization

paper · pdf · doi:10.48550/arxiv.2103.04866

Abstract

We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts they define are not topologically mixing. We then show that they satisfy a weaker mixing property using a numeration system arising from a sequence of lengths of inflated words. Moreover, we provide explicit bounds for the corresponding topological entropy in terms of the defining parameters n and p.

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