Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups BS(1,n)

Nathalie Aubrun; Michael Schraudner

doi:10.5802/crmath.571

Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups BS(1,n)

Titre traduit de la contribution: Pavages hyperboliques engendrés par une substitution comme sous-décalages de type fini sur les groupes de Baumslag–Solitar BS(1, n)

Nathalie Aubrun
, Michael Schraudner

INRIA Saclay, Laboratoire de Recherche en Informatique (LRI), Université Paris Sud
University of Chile

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We present a technique to lift some tilings of the discrete hyperbolic plane –tilings defined by a 1D substitution– into a zero entropy subshift of finite type (SFT) on non-abelian amenable groups BS(1,n) for n ≥ 2. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal.

Titre traduit de la contribution	Pavages hyperboliques engendrés par une substitution comme sous-décalages de type fini sur les groupes de Baumslag–Solitar BS(1, n)
langue originale	Anglais
Pages (de - à)	553-580
Nombre de pages	28
journal	Comptes Rendus Mathematique
Volume	362
Les DOIs	https://doi.org/10.5802/crmath.571
état	Publié - 1 janv. 2024
Modification externe	Oui

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10.5802/crmath.571

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abstract = "We present a technique to lift some tilings of the discrete hyperbolic plane –tilings defined by a 1D substitution– into a zero entropy subshift of finite type (SFT) on non-abelian amenable groups BS(1,n) for n ≥ 2. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal.",

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AB - We present a technique to lift some tilings of the discrete hyperbolic plane –tilings defined by a 1D substitution– into a zero entropy subshift of finite type (SFT) on non-abelian amenable groups BS(1,n) for n ≥ 2. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal.

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Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups BS(1,n)

Résumé

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