Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies

Baake, Michael; Lenz, Daniel; Richard, Christoph

Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies

Authors

Baake, Michael

Lenz, Daniel

Richard, Christoph

Description

Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy 0 if it has uniform cluster frequencies and is pure point diffractive. We also note that the patch counting entropy is 0 whenever the repetitivity function satisfies a certain growth restriction.
16 pages; revised and slightly expanded version