arXiv subjects
Publications and source records attributed to Jamal Drewlo.
We show a continuity result for the Weyl pseudometric on subshifts which are generated by model sets. This fact is then used for multiple constructions of subshifts that exhibit different behavior regarding entropy, amorphic complexity and their maximal equicontinuous factor.
We show a one-to-one correspondence between Toeplitz arrays over residually finite topological groups and model sets obtained via specific cut and project schemes, built from the odometer associated to the Toeplitz array. As an application, we construct irregular Toeplitz arrays which are extensions of maximal rank $k$ over their maximal equicontinuous factor (given by the associated odometer) and have exactly $k$ different ergodic measures. A modification of the construction also allows to obtain examples with the same measure-theoretic structure, but infinite maximal rank.
In this work, we present a self-contained construction that proves the existence of strictly ergodic Toeplitz $\mathbb{Z}^d$-subshifts with arbitrary prescribed entropy. Moreover, any of these constructed subshifts will have the same maximal equicontinuous factor, which is the universal odometer over $\mathbb{Z}^d$.