Equicontinuous Factors, Proximality and Ellis Semigroup for Delone Sets

Jean-Baptiste Aujogue (1) , Marcy Barge (2) , Johannes Kellendonk (3, 1) , Daniel Lenz (4)

1 PSPM - Probabilités, statistique, physique mathématique
2 Department of Mathematical Sciences [Missoula]
3 ICJ - Institut Camille Jordan
4 Fakultat fur Mathematik

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

Domaines: Systèmes dynamiques [math.DS]

Jean-Baptiste Aujogue, Marcy Barge, Johannes Kellendonk, Daniel Lenz. Equicontinuous Factors, Proximality and Ellis Semigroup for Delone Sets. Mathematics of Aperiodic Order, 309, Birkhäuser, Basel, pp.137-194, 2015, Progress in Mathematics. ⟨hal-02106329⟩