Tame or wild Toeplitz shifts
Dynamical Systems
2024-05-08 v2
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 subshifts. A body of elaborate examples shows that the assumptions of our results cannot be relaxed.
Keywords
Cite
@article{arxiv.2010.11128,
title = {Tame or wild Toeplitz shifts},
author = {Gabriel Fuhrmann and Johannes Kellendonk and Reem Yassawi},
journal= {arXiv preprint arXiv:2010.11128},
year = {2024}
}
Comments
30 pages, 3 figures. Minor revisions of the first version