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)

Nathalie Aubrun
, Michael Schraudner

Research output: Contribution to journal › Article › peer-review

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.

Translated title of the contribution	Pavages hyperboliques engendrés par une substitution comme sous-décalages de type fini sur les groupes de Baumslag–Solitar BS(1, n)
Original language	English
Pages (from-to)	553-580
Number of pages	28
Journal	Comptes Rendus Mathematique
Volume	362
DOIs	https://doi.org/10.5802/crmath.571
Publication status	Published - 1 Jan 2024
Externally published	Yes

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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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DO - 10.5802/crmath.571

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JO - Comptes Rendus Mathematique

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ER -

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

Abstract

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