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Tame or wild Toeplitz shifts

Fuhrmann, G.; Kellendonk, J.; Yassawi, R.

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Authors

J. Kellendonk

R. Yassawi



Abstract

We investigate tameness of Toeplitz shifts. By introducing the notion of extended Bratteli–Vershik diagrams, we show that such shifts with finite Toeplitz rank are tame if and only if there are at most countably many orbits of singular fibres over the maximal equicontinuous factor. The ideas are illustrated using the class of substitution shifts. A body of elaborate examples shows that the assumptions of our results cannot be relaxed.

Citation

Fuhrmann, G., Kellendonk, J., & Yassawi, R. (2023). Tame or wild Toeplitz shifts. Ergodic Theory and Dynamical Systems, https://doi.org/10.1017/etds.2023.58

Journal Article Type Article
Acceptance Date Jul 7, 2023
Online Publication Date Aug 18, 2023
Publication Date Aug 18, 2023
Deposit Date Aug 31, 2021
Publicly Available Date Aug 22, 2023
Journal Ergodic Theory and Dynamical Systems
Print ISSN 0143-3857
Publisher Cambridge University Press
DOI https://doi.org/10.1017/etds.2023.58
Public URL https://durham-repository.worktribe.com/output/1236325
Related Public URLs https://arxiv.org/abs/2010.11128

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