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Geometrical representation of subshifts for primitive substitutions
Part of:
Topological dynamics
Published online by Cambridge University Press: 03 November 2023
Abstract
For any primitive substitution whose Perron eigenvalue is a Pisot unit, we construct a domain exchange that is measurably conjugate to the subshift. Additionally, we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitutions, we show that the subshift is either a finite extension of a torus translation or its eigenvalues are roots of unity. Furthermore, we provide an algorithm to compute eigenvalues of the subshift associated with any primitive pseudo-unimodular substitution.
Keywords
MSC classification
Primary:
37B10: Symbolic dynamics
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- Original Article
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- © The Author(s), 2023. Published by Cambridge University Press
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