Invariant Measures on Stationary Bratteli Diagrams

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the Vershik map). These measures are completely described by the incidence matrix of the diagram. Since such diagrams correspond to substitution dynamical systems, this description gives an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.
40 pages. Exposition is reworked

Keywords

Dynamical Systems, 37B05; 54H20

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/225391

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.1088
 http://arxiv.org/abs/0812.1088

Collections

arXiv