Cantor aperiodic systems and Bratteli diagrams

Konstantin Medynets

doi:10.1016/j.crma.2005.10.024

Dynamical Systems

Cantor aperiodic systems and Bratteli diagrams
[Les systèmes de Cantor apériodiques et les diagrammes de Bratteli]

Présenté par : Étienne Ghys

Konstantin Medynets ¹

¹ Institute for Low Temperature Physics, 61103 Kharkov, Ukraine

Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 43-46.

Résumé
Abstract

Nous démontrons que chaque système de Cantor apériodique est homéomorphe à une application de Vershik agissant dans l'espace de chemins infinis d'un diagramme de Bratteli ordonné et donnons quelques applications de ce résultat.

We prove that every Cantor aperiodic system is homeomorphic to the Vershik map acting on the space of infinite paths of an ordered Bratteli diagram and give several corollaries of this result.

Reçu le : 2005-08-15
Accepté le : 2005-10-19
Publié le : 2005-11-28

DOI : 10.1016/j.crma.2005.10.024

Affiliations des auteurs :

Konstantin Medynets ¹

¹ Institute for Low Temperature Physics, 61103 Kharkov, Ukraine

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Konstantin Medynets. Cantor aperiodic systems and Bratteli diagrams. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 43-46. doi : 10.1016/j.crma.2005.10.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.024/

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