Model sets with positive entropy in Euclidean cut and project schemes

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have empty interior. In a probabilistic construction, the entrop...

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Bibliographic Details
Published in:arXiv.org 2018-06
Main Authors: Jäger, Tobias, Lenz, Daniel, Oertel, Christian
Format: Article
Language:English
Subjects:
Entropy
Online Access:Get full text
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Summary:We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have empty interior. In a probabilistic construction, the entropy almost surely turns out to be proportional to the measure of the boundary of the window.
ISSN:2331-8422