Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T06:06:47.830Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)