2020/12/20 by Nathalie Aubrun, Aubrun, Nathalie, Michael Schraudner +1
Computer Science · Mathematics · #Cellular Automata and Applications #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #cs.DM #math.DS #math.GR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2012.11037
arxiv created 2020/12/20 · openalex publication_date 2020/12/20 · openalex created_date 2020/12/21 · arxiv updated 2020/12/22 · openalex updated_date 2026/07/28
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 ℤ2 or Goodman-Strauss's on ℍ2.