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Geometrical representation of subshifts for primitive substitutions

Part of: Topological dynamics

Published online by Cambridge University Press:  03 November 2023

PAUL MERCAT
PAUL MERCAT*
Affiliation:
I2M, Aix-Marseille University, 3 Place Victor Hugo, 13331 Marseille, France
*
e-mail: [email protected]
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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

substitution subshiftsRauzy fractalsfinite extension of torus translationeigenvalues of subshifts

MSC classification

Primary: 37B10: Symbolic dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 7 , July 2024 , pp. 1885 - 1912
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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