Comptes Rendus
no. 1
Dynamical Systems
Cantor aperiodic systems and Bratteli diagrams
[Les systèmes de Cantor apériodiques et les diagrammes de Bratteli]

Présenté par : Étienne Ghys

Konstantin Medynets1
1 Institute for Low Temperature Physics, 61103 Kharkov, Ukraine
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 43-46.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.024
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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[3] F. Durand; B. Host; C. Skau Substitutional dynamical systems, Bratteli diagrams and dimension groups, Ergodic Theory Dynam. Systems, Volume 19 (1999), pp. 953-993

[4] T. Giordano; I. Putnam; C. Skau Topological orbit equivalence and C∗-crossed products, J. Reine Angew. Math., Volume 469 (1995), pp. 51-111

[5] T. Giordano; I. Putnam; C. Skau Affable equivalence relations and orbit structure of Cantor dynamical systems, Ergodic Theory Dynam. Systems, Volume 24 (2004), pp. 441-475

[6] E. Glasner; B. Weiss Weak orbit equivalence of Cantor minimal systems, Int. J. Math., Volume 6 (1995) no. 4, pp. 559-579

[7] R.H. Herman; I. Putnam; C. Skau Ordered Bratteli diagram, dimension groups, and topological dynamics, Int. J. Math., Volume 3 (1992), pp. 827-864

[8] H. Matui Topological orbit equivalence of locally compact Cantor minimal systems, Ergodic Theory Dynam. Systems, Volume 22 (2002) no. 6, pp. 1871-1903

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