A note on entropy of Delone sets

Till Hauser

Mathematische Nachrichten, 2022, vol. 295, issue 8, 1513-1532

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.

Date: 2022
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