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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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 $\mathbb{H}^2$. |
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| ISSN: | 1778-3569 |