Geometric representation of substitutions of Pisot type

By V. Canterini, Anne Siegel. 2001

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Atomic surfaces, tilings and coincidence I. irreducible case (2006, background): “The atomic surfaces, also called Rauzy fractals, of irreducible and unimodular Pisot substitutions have been studied extensively by many authors([Rau, Luc, AI, SW, IR1, IR2, Sie1, Sie2, BD, CS , Pra, HZ]).”
Tilings associated with beta-numeration and substitutions. (2005, background): “The first one is based on formal power series seen as digit expansions such as (1), and is inspired by the seminal paper [Rau82]; see e.g., [Aki99, Aki98, Aki02, CS01a, CS01b , Sie03, Mes98, Mes00].”
Beyond substitutive dynamical systems: S-adic expansions (2013, background): “There exist deep relations between substitutive dynamical systems and shifts of finite type and we refer to [51, 52] and \lfloor 116 , Chap.”
Topological Properties of Rauzy Fractals (2010, background): “From Rauzy’s seminal paper [110], generalizations of the construction have been proposed in different contexts: starting from the investigation of irreducible Pisot units [25, 49, 96, 97], reducible Pisot units and beta-numeration [5, 7, 123], the case of non-unit Pisot numbers [39, 118] and the hyp”