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

12/20/2020

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by   Nathalie Aubrun, et al.

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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 Baumslag-Solitar groups BS(1,n) for n≥2. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal. As an application we construct a strongly aperiodic SFT on BS(1,n) with a hierarchical structure, which is an analogue of Robinson's construction on ℤ^2 or Goodman-Strauss's on ℍ_2.