Equicontinuous factors, proximality and Ellis semigroup for Delone sets

TL;DR

This paper explores the dynamical properties of Delone sets and tilings, focusing on their equicontinuous factors, proximality, and Ellis semigroup, to deepen understanding of their topological dynamics.

Contribution

It introduces new insights into the structure of Delone dynamical systems by analyzing their maximal equicontinuous factors, proximality relations, and enveloping semigroups.

Findings

Characterization of maximal equicontinuous factors for Delone sets

Analysis of proximality relations in tiling dynamical systems

Description of Ellis semigroup structure for these systems

Abstract

We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings. We consider in particular, the maximal equicontinuous factor of a Delone dynamical system, the proximality relation and the enveloping semigroup of such systems.