Random product of substitutions with the same incidence matrix

Pierre Arnoux (1) , Masahiro Mizutani (2) , Tarek Sellami (3)

1 I2M - Institut de Mathématiques de Marseille
2 Daito Bunka University
3 Université de Sfax - University of Sfax

Any infinite sequence of substitutions with the same matrix of the Pisot type defines a symbolic dynamical system which is minimal. We prove that, to any such sequence, we can associate a compact set (Rauzy fractal) by projection of the stepped line associated with an element of the symbolic system on the contracting space of the matrix. We show that this Rauzy fractal depends continuously on the sequence of substitutions, and investigate some of its properties; in some cases, this construction gives a geometric model for the symbolic dynamical system.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Pierre Arnoux, Masahiro Mizutani, Tarek Sellami. Random product of substitutions with the same incidence matrix. Theoretical Computer Science, 2014, 543, pp.68-78. ⟨10.1016/j.tcs.2014.06.002⟩. ⟨hal-01113397⟩