Aperiodic substitutional systems and their Bratteli diagrams

S Bezuglyi; J Kwiatkowski; K Medynets

doi:10.48550/arxiv.0705.4080

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Aperiodic substitutional systems and their Bratteli diagrams

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Aperiodic substitutional systems and their Bratteli diagrams

S Bezuglyi, J Kwiatkowski and K Medynets

ArXiv.org

Cornell University

05/28/2007

DOI: 10.48550/arxiv.0705.4080

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional system if and only if no restriction of to a minimal component is homeomorphic to an odometer. We also show that every aperiodic substitutional system generated by a substitution with nesting property is homeomorphic to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitutional system is recognizable. The classes of -primitive substitutions and associated to them derivative substitutions are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.

Mathematics - Dynamical Systems

Details

Title: Subtitle: Aperiodic substitutional systems and their Bratteli diagrams
Creators: S Bezuglyi
J Kwiatkowski
K Medynets
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.0705.4080
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 05/28/2007
Academic Unit: Mathematics
Record Identifier: 9984936603702771

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