Conjugacy of Unimodular Pisot Substitution Subshifts to Domain Exchanges
[Conjugaison des sous-décalages de substitutions Pisot unimodulaires à des échanges de domaines]
Durand, Fabien1 ; Petite, Samuel1
1 Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France
Annales Henri Lebesgue, Tome 6 (2023), pp. 1259-1289

We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in a Euclidean space which is a finite topological extension of a translation on a torus. This generalizes the pioneer works of Rauzy and Arnoux–Ito providing geometric realizations to any unimodular Pisot substitution without any additional combinatorial condition.

Nous prouvons que tout sous-décalage de substitution Pisot unimodulaire est mesurablement conjugué à un échange de domaine dans un espace euclidien qui est une extension topologique finie d’une translation sur un tore. Ceci étend les travaux pionniers de Rauzy et Arnoux–Ito sur les réalisations géométriques à toutes les substitutions de type Pisot unimodulaires sans aucune condition combinatoire supplémentaire.

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DOI : 10.5802/ahl.188
Classification : 37B10, 37B20
Keywords: minimal Cantor systems, subshifts, domain exchanges, geometric realizations, eigenvalues, Pisot conjecture, substitutions

Durand, Fabien 1 ; Petite, Samuel 1

1 Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Conjugacy of {Unimodular} {Pisot} {Substitution} {Subshifts} to {Domain} {Exchanges}},
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Durand, Fabien; Petite, Samuel. Conjugacy of Unimodular Pisot Substitution Subshifts to Domain Exchanges. Annales Henri Lebesgue, Tome 6 (2023), pp. 1259-1289. doi: 10.5802/ahl.188

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