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ISSN 1088-6850(e) ISSN 0002-9947(p)

Geometric representation of substitutions of Pisot type

Author(s): Vincent Canterini; Anne Siegel
Journal: Trans. Amer. Math. Soc. 353 (2001), 5121-5144.
MSC (2000): Primary 37B10, 28A80; Secondary 47A35
Posted: July 13, 2001
MathSciNet review: 1852097
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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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