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Geometric representation of substitutions of Pisot type. (English) Zbl 1142.37302
Summary: We prove that a substitutive dynamical system of Pisot type contains a factor which is isomorphic to a minimal rotation on a torus. If the substitution is unimodular and satisfies a certain combinatorial condition, we prove that the dynamical system is measurably conjugate to an exchange of domains in a self-similar compact subset of the Euclidean space.

MSC:
37B10 Symbolic dynamics
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