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abstract: 'This work deals with certain point patterns of an Euclidean space, for which the calculation of the Ellis enveloping semigroup of their associated dynamical systems is performed. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the underlying space, are explicitly described. The present work is illustrated with the treatment of the vertex pattern of the so-called Amman-Beenker tiling of the plane.'
author:
- 'Jean-Baptiste Aujogue'
title: Ellis enveloping semigroup for almost canonical model sets
---

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This article proposes to study certain aspects of dynamical systems which are associated with *point patterns* of an Euclidean space. The topic of point patterns takes its origins in symbolic dynamic, and concerns also aperiodic tillings. It has however been increasingly addressed by numerous authors since these past thirty years after the discovery by Schetchmann et al. of physical materials now commonly called *Quasicrystals*. In this context a point pattern of an Euclidean space $\mathbb{R}^d$ is thought as an alloy, where points are understood as positions of atoms, or molecules or electrons, and the quasicrystalline structure then comes when a certain *long range order* is observed on the disposition of points within the 