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arXiv · 0706.1677

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

Michael Baake·Daniel Lenz·Christoph Richard
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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.

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Michael Baake, Daniel Lenz, Christoph Richard. 2007-09-14. Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies. https://doi.org/10.1007/s11005-007-0186-7

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