Abstract
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.
Funder
HORIZON EUROPE Marie Sklodowska-Curie Actions
Engineering and Physical Sciences Research Council
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics