Toeplitz flows and model sets

Abstract

We show that binary Toeplitz flows can be interpreted as Delone dynamical systems induced by model sets and analyse the quantitative relations between the respective system parameters. This has a number of immediate consequences for the theory of model sets. In particular, we use our results in combination with special examples of irregular Toeplitz flows from the literature to demonstrate that irregular proper model sets may be uniquely ergodic and do not need to have positive entropy. This answers questions by Schlottmann and Moody.

9 pages, slightly updated version

References in corpus (2)

• Eigenvalues of Toeplitz minimal systems of finite topological rank
• Model sets with positive entropy in Euclidean cut and project schemes

Cited by in corpus (6)

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• Combinatorics of One-Dimensional Simple Toeplitz Subshifts
• Amorphic complexity of group actions with applications to quasicrystals