Ellis enveloping semigroup for almost canonical model sets of an Euclidean space

Abstract

We consider certain point patterns of an Euclidean space and calculate the Ellis enveloping semigroup of their associated dynamical systems. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the underlying space, are explicitly described. As an example, we treat the vertex pattern of the Amman-Beenker tiling of the plane.

44 pages. This version is the one published by Algebraic & Geometric Topology after revisions

References in corpus (2)

• Pure Point Dynamical and Diffraction Spectra
• Integral cohomology of rational projection method patterns

Cited by in corpus (4)

• On tameness of almost automorphic dynamical systems for general groups
• Combinatorial independence and naive entropy
• Tame or wild Toeplitz shifts
• Complete regularity of Ellis semigroups of $\mathbb{Z}$-actions