Geometric representation of substitutions of Pisot type

Canterini, Vincent; Siegel, Anne

doi:10.1090/S0002-9947-01-02797-0

Geometric representation of substitutions of Pisot type
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by Vincent Canterini and Anne Siegel PDF

Trans. Amer. Math. Soc. 353 (2001), 5121-5144 Request permission

Abstract:

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.

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