Keller G (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 40
Pages Range: 6855-6875
Journal Issue: 12
DOI: 10.3934/dcds.2020132
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.
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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