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dc.contributor.authorFuhrmann, Gabriel
dc.contributor.authorGröger, Maik
dc.contributor.authorJäger, Tobias
dc.contributor.authorKwietniak, Dominik
dc.date.accessioned2021-02-02T07:31:53Z
dc.date.available2021-02-02T07:31:53Z
dc.date.issued2021-02-02
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3830
dc.description.abstractIn 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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2021-03
dc.titleAmorphic Complexity of Group Actions with Applications to Quasicrystalsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2021-03
local.scientificprogramResearch in Pairs 2017
local.series.idOWP-2021-03en_US


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