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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146170Delone 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 versionDynamical SystemsCombinatorics37A35, 37B40, 52C23Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequenciestext