dc.contributor.author Fuhrmann, Gabriel dc.contributor.author Gröger, Maik dc.contributor.author Jäger, Tobias dc.contributor.author Kwietniak, Dominik dc.date.accessioned 2021-02-02T07:31:53Z dc.date.available 2021-02-02T07:31:53Z dc.date.issued 2021-02-02 dc.identifier.uri http://publications.mfo.de/handle/mfo/3830 dc.description.abstract In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We show that it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone dynamical systems related to regular model sets obtained via Meyer's cut and project method. We provide sharp upper bounds on amorphic complexity of such systems. In doing so, we observe an intimate relationship between amorphic complexity and fractal geometry. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2021-03 dc.title Amorphic Complexity of Group Actions with Applications to Quasicrystals en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2021-03 local.scientificprogram Research in Pairs 2017 local.series.id OWP-2021-03 en_US dc.identifier.urn urn:nbn:de:101:1-2021030910405341225645 dc.identifier.ppn 1751086577
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