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Realization of a Choquet simplex as the set of invariant probability measures of a tiling system

Published online by Cambridge University Press:  11 September 2006

MARIA ISABEL CORTEZ
MARIA ISABEL CORTEZ
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile Casilla 170/3 correo 3, Santiago, Chile and Centro de Modelamiento Matemático, Av. Blanco Encalada 2120 Piso 7, Santiago de Chile, Chile (e-mail: mcortez@dim.uchile.cl)
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Abstract

In this paper we show that, for every Choquet simplex $K$ and for every $d>1$, there exists a ${\mathbb Z}^d$-Toeplitz system whose set of invariant probability measures is affine homeomorphic to $K$. Then, we conclude that $K$ may be realized as the set of invariant probability measures of a tiling system $(\Omega_T,{\mathbb R}^d)$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1417 - 1441
Copyright
2006 Cambridge University Press

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