Work

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

Year: 2024

Type: article

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. 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 .

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.571

Authors: Nathalie Aubrun, Michael Schraudner

Institutions: Université Paris-Saclay, Laboratoire Interdisciplinaire des Sciences du Numérique, Center for Mathematical Modeling

Language: Latvian

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: G5420063140, Computational and Combinatorial aspects of Symbolic Dynamics on Groups.