Journal article
Aperiodic substitution systems and their bratteli diagrams
Ergodic Theory and Dynamical Systems, Vol.29(1), pp.37-72
2009
DOI: 10.1017/S0143385708000230
Abstract
Abstract We study aperiodic substitution dynamical systems arising from non-primitive substitutions. We prove that the Vershik homeomorphism φ of a stationary ordered Bratteli diagram is topologically conjugate to an aperiodic substitution system if and only if no restriction of φ to a minimal component is conjugate to an odometer. We also show that every aperiodic substitution system generated by a substitution with nesting property is conjugate to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitution system is recognizable. The classes of m -primitive substitutions and derivative substitutions associated with them are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.
Details
- Title: Subtitle
- Aperiodic substitution systems and their bratteli diagrams
- Creators
- S BezuglyiK MedynetsJ Kwiatkowski
- Resource Type
- Journal article
- Publication Details
- Ergodic Theory and Dynamical Systems, Vol.29(1), pp.37-72
- DOI
- 10.1017/S0143385708000230
- ISSN
- 1469-4417
- eISSN
- 1469-4417
- Language
- English
- Date published
- 2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983985961402771
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