Abstract: | In this article we study the common dynamics of two different Pisot substitutions σ
1 and σ
2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions
σ
1 and σ
2. Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function
systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems
which describe the common dynamics. We also consider generalizations of these results to the nonunimodular case, the case
of more than two substitutions and the case of two substitutions with different incidence matrices. |