Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$
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 $\mathit{BS}(1,n)$ for $n\ge 2$. For well chosen hyperbolic tilings, this SFT is also aperiodic and min...
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| Format: | Article |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.571/ |
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| author | Aubrun, Nathalie Schraudner, Michael |
| author_facet | Aubrun, Nathalie Schraudner, Michael |
| author_sort | Aubrun, Nathalie |
| collection | DOAJ |
| description | 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 $\mathit{BS}(1,n)$ for $n\ge 2$. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal. As an application we construct a strongly aperiodic SFT on $\mathit{BS}(1,n)$ with a hierarchical structure, which is an analogue of Robinson’s construction on $\mathbb{Z}^2$ or Goodman–Strauss’s on $\mathbb{H}^2$. |
| format | Article |
| id | doaj-art-aa0bf4e877584e26a9076e986562ba61 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-aa0bf4e877584e26a9076e986562ba612025-02-07T11:21:12ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G555358010.5802/crmath.57110.5802/crmath.571Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$Aubrun, Nathalie0https://orcid.org/0000-0002-2701-570XSchraudner, Michael1Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400, Orsay, FranceCentro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de ChileWe 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 $\mathit{BS}(1,n)$ for $n\ge 2$. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal. As an application we construct a strongly aperiodic SFT on $\mathit{BS}(1,n)$ with a hierarchical structure, which is an analogue of Robinson’s construction on $\mathbb{Z}^2$ or Goodman–Strauss’s on $\mathbb{H}^2$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.571/ |
| spellingShingle | Aubrun, Nathalie Schraudner, Michael Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ Comptes Rendus. Mathématique |
| title | Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ |
| title_full | Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ |
| title_fullStr | Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ |
| title_full_unstemmed | Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ |
| title_short | Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $\mathit{BS}(1,n)$ |
| title_sort | tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on baumslag solitar groups mathit bs 1 n |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.571/ |
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