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Geometric representation of substitutions of Pisot type


Authors: Vincent Canterini and Anne Siegel
Journal: Trans. Amer. Math. Soc. 353 (2001), 5121-5144
MSC (2000): Primary 37B10, 28A80; Secondary 47A35
DOI: https://doi.org/10.1090/S0002-9947-01-02797-0
Published electronically: 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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Additional Information

Vincent Canterini
Affiliation: Institut de Mathématiques de Luminy, UPR 9016, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 9, France
Address at time of publication: CESAME, Université Catholique de Louvain, Bâtiment Euler, Avenue G. Lemairè, 4, 1348 Louvain-la-Neuve, Belgium
Email: canterini@anma.ucl.ac.be

Anne Siegel
Affiliation: Institut de Mathématiques de Luminy, UPR 9016, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 9, France
Email: siegel@iml.univ-mrs.fr

DOI: https://doi.org/10.1090/S0002-9947-01-02797-0
Keywords: Substitutive dynamical system, toral translation, factor map, domain exchange
Received by editor(s): February 1, 2000
Received by editor(s) in revised form: August 12, 2000
Published electronically: July 13, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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