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A note on entropy of Delone sets

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  • Till Hauser

Abstract

In this note we present that the patch counting entropy can be obtained as a limit and investigate which sequences of compact sets are suitable to define this quantity. We furthermore present a geometric definition of patch counting entropy for Delone sets of infinite local complexity and that the patch counting entropy of a Delone set equals the topological entropy of the corresponding Delone dynamical system. We present our results in the context of (non‐compact) locally compact abelian groups that contain Meyer sets.

Suggested Citation

  • Till Hauser, 2022. "A note on entropy of Delone sets," Mathematische Nachrichten, Wiley Blackwell, vol. 295(8), pages 1513-1532, August.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:8:p:1513-1532
    DOI: 10.1002/mana.202000063
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