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Geometric representation of substitutions of Pisot type |
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| Authors: | Vincent Canterini Anne Siegel |
| Affiliation: | Institut de Mathématiques de Luminy, UPR 9016, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 9, France ; Institut de Mathématiques de Luminy, UPR 9016, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 9, France |
| 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. |
| Keywords: | Substitutive dynamical system toral translation factor map domain exchange |
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