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

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

2007-06-12

arxiv.org/abs/0706.1677v2

Lett. Math. Phys. 82 (2007) 61-77

Mathematics

Dynamical Systems

16 pages; revised and slightly expanded version

Scientific paper

10.1007/s11005-007-0186-7

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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