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On weak model sets of extremal density

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dc.contributor.authorBaake, Michael
dc.contributor.authorHuck, Christian
dc.contributor.authorStrungaru, Nicolae
dc.date.accessioned2021-01-14
dc.date.accessioned2022-05-31T01:43:06Z
dc.date.available2022-05-31T01:43:06Z
dc.date.issued2016
dc.description.abstractThe theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a boundary of positive measure, or even consists of boundary only. The latter phenomena are related to the topological entropy of the corresponding dynamical system and to various other unusual properties. Under a rather natural extremality assumption on the density of the weak model set we establish its pure point diffraction nature. We derive an explicit formula that can be seen as the generalisation of the case of regular model sets. Furthermore, the corresponding natural patch frequency measure is shown to be ergodic. Since weak model sets of extremal density are generic for this measure, one obtains that the dynamical spectrum of the hull is pure point as well.
dc.format.extent1.80MB
dc.format.mimetypePDF
dc.identifier.citationBaake, M., Huck, C., & Strungaru, N. (2016). On weak model sets of extremal density. arXiv:1512.07129v2. https://arxiv.org/abs/1512.07129
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2133
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjectweak model sets
dc.subjectvisible lattice points
dc.subjectpositive measure
dc.subjectdensity
dc.titleOn weak model sets of extremal densityen
dc.typeReport
dspace.entity.type

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