Tame or wild Toeplitz shifts

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

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, 44(5), 1379-1417. 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
• Electronic ISSN: 1469-4417
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 44
• Issue: 5
• Pages: 1379-1417
• 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