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- W4287588788 abstract "For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the setting of sigma-compact locally compact Abelian groups and show that the topological entropy of the associated Delone dynamical system is zero. For this we provide a suitable version of the variational principle. We furthermore construct counterexamples, which show that the patch counting entropy of such sets can be non-zero in this context. Other counterexamples will show that the patch counting entropy of such a set can not be computed along a limit and even be infinite in this setting." @default.
- W4287588788 created "2022-07-25" @default.
- W4287588788 creator A5020567885 @default.
- W4287588788 date "2020-11-25" @default.
- W4287588788 modified "2023-10-17" @default.
- W4287588788 title "Pure point diffraction and entropy beyond the Euclidean space" @default.
- W4287588788 doi "https://doi.org/10.48550/arxiv.2011.12880" @default.
- W4287588788 hasPublicationYear "2020" @default.
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