Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag–Solitar groups $BS(1,n)$ - Aubrun, Nathalie; Schraudner, Michael (Comptes Rendus. Mathématique)
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 $n\ge 2$. 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 $\mathbb{Z}^2$ or Goodman–Strauss’s on $\mathbb{H}^2$.