Geometric representation of substitutions of Pisot type

Authors
Canterini, V Siegel, A
Citation
V. Canterini et A. Siegel, Geometric representation of substitutions of Pisot type, T AM MATH S, 353(12), 2001, pp. 5121-5144
Citations number
32
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
353
Issue
12
Year of publication
2001
Pages
5121 - 5144
Database
ISI
SICI code
0002-9947(2001)353:12<5121:GROSOP>2.0.ZU;2-A
Abstract
We prove that a substitutive dynamical system of Pisot type contains a fact or which is isomorphic to a minimal rotation on a torus. If the substitutio n is unimodular and satisfies a certain combinatorial condition, we prove t hat the dynamical system is measurably conjugate to an exchange of domains in a self-similar compact subset of the Euclidean space.