Irregular model sets and tame dynamics

We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly positive. Extending the proof to a more general setting, we...

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Bibliographic Details
Published in:arXiv.org 2018-11
Main Authors: Fuhrmann, Gabriel, Glasner, Eli, Jäger, Tobias, Oertel, Christian
Format: Article
Language:English
Subjects:
Entropy
Topology
Online Access:Get full text
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Summary:We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly positive. Extending the proof to a more general setting, we further obtain that tame implies regular for almost automorphic group actions on compact spaces. In the converse direction, we show that even in the restrictive case of Euclidean cut and project schemes irregular model sets may be uniquely ergodic and have zero topological entropy. This provides negative answers to questions by Schlottmann and Moody in the Euclidean setting.
ISSN:2331-8422