Common dynamics of two Pisot substitutions with the same incidence matrix
نویسندگان
چکیده
The matrix of a substitution is not sufficient to completely determine the dynamics associated with it, even in the simplest cases since there are many words with the same abelianization. In this paper we study the common points of the canonical broken lines associated with two different irreducible Pisot unimodular substitutions σ1 and σ2 having the same incidence matrix. We prove that if 0 is an inner point to the Rauzy fractal associated with the substitution σ1 and σ1 verifies the Pisot conjecture then these common points can be generated with a substitution on an alphabet of socalled balanced pairs, and we obtain in this way the intersection of the interior of two Rauzy fractals.
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