Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
Dynamical Systems
2008-01-19 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.0706.1677,
title = {Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies},
author = {Michael Baake and Daniel Lenz and Christoph Richard},
journal= {arXiv preprint arXiv:0706.1677},
year = {2008}
}