# MAXIMAL EQUICONTINUOUS GENERIC FACTORS AND WEAK MODEL SETS

Keller G (2020)

**Publication Type:** Journal article

**Publication year:** 2020

### Journal

**Book Volume:** 40

**Pages Range:** 6855-6875

**Journal Issue:** 12

**DOI:** 10.3934/dcds.2020132

### Abstract

The orbit closures of regular model sets generated from a cut-and-project scheme given by a co-compact lattice L subset of G x H and compact and aperiodic window W subset of H, have the maximal equicontinuous factor (MEF) (G x H)/L, if the window is toplogically regular. This picture breaks down, when the window has empty interior, in which case the MEF is trivial, although (G x H)/L continues to be the Kronecker factor for the Mirsky measure. As this happens for many interesting examples like the square-free numbers or the visible lattice points, a weaker concept of topological factors is needed, like that of generic factors [24]. For topological dynamical systems that possess a finite invariant measure with full support (E-systems) we prove the existence of a maximal equicontinuous generic factor (MEGF) and characterize it in terms of the regional proximal relation. This part of the paper profits strongly from previous work by McMahon [33] and Auslander [2]. In Sections 3 and 4 we determine the MEGF of orbit closures of weak model sets and use this result for an alternative proof (of a generalization) of the fact [34] that the centralizer of any B-free dynamical system of Erdos type is trivial.

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### How to cite

**APA:**

Keller, G. (2020). MAXIMAL EQUICONTINUOUS GENERIC FACTORS AND WEAK MODEL SETS. *Discrete and Continuous Dynamical Systems*, *40*(12), 6855-6875. https://dx.doi.org/10.3934/dcds.2020132

**MLA:**

Keller, Gerhard. "MAXIMAL EQUICONTINUOUS GENERIC FACTORS AND WEAK MODEL SETS." *Discrete and Continuous Dynamical Systems* 40.12 (2020): 6855-6875.

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