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arXiv · 0705.4080

Aperiodic substitutional systems and their Bratteli diagrams

S. Bezuglyi·J. Kwiatkowski·K. Medynets
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Abstract

In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism $ϕ$ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional system if and only if no restriction of $ϕ$ 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 $m$-primitive substitutions and associated to them derivative substitutions are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.

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S. Bezuglyi, J. Kwiatkowski, K. Medynets. 2007-05-28. Aperiodic substitutional systems and their Bratteli diagrams. https://arxiv.org/abs/0705.4080

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