# A Note on Entropy of Delone Sets

## TL;DR

This paper explores the entropy of Delone sets, providing a geometric definition and establishing its equivalence with topological entropy within the framework of locally compact Abelian groups containing Meyer sets.

## Contribution

It introduces a geometric approach to patch counting entropy for Delone sets with infinite local complexity and links it to topological entropy of associated dynamical systems.

## Key findings

- Patch counting entropy can be obtained as a limit.
- Geometric definition of entropy for Delone sets with infinite local complexity.
- Entropy of Delone sets equals the topological entropy of the dynamical system.

## 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.