Geometry of the common dynamics of Pisot substitutions with the same incidence matrix
Tarek Sellami · Comptes Rendus Mathématique · 2010
Any Pisot substitution can be associated with a bounded set with interesting properties, called the Rauzy fractal. This set is obtained by projection of the broken line associated with an infinite fixed point. Two substitutions having the same incidence matrix can have different Rauzy fractals. We show that under weak conditions, the intersection of these two fractals has strictly positive measure, and can also be generated by a substitution.