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arXiv · 2201.01268

Geometrical representation of subshifts for primitive substitutions

Paul Mercat
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Abstract

For any primitive substitution whose Perron eigenvalue is Pisot unit, we construct a domain exchange measurably conjugated to the subshift. And we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitution, we show that the subshift is either a finite extension of a torus translation, either a power of the subshift is weakly mixing. And we provide an algorithm to compute eigenvalues of the subshift associated to any primitive pseudo-unimodular substitution.

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Paul Mercat. 2022-01-04. Geometrical representation of subshifts for primitive substitutions. https://doi.org/10.1017/etds.2023.101

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