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dc.contributor.authorHare, Kathryn
dc.contributor.authorRutar, Alex
dc.date.accessioned2022-09-16T14:30:09Z
dc.date.available2022-09-16T14:30:09Z
dc.date.issued2022-08-11
dc.identifier281147528
dc.identifierb4c69f18-e830-4ce2-bae2-4890582f5909
dc.identifier85137241538
dc.identifier000842713100001
dc.identifier.citationHare , K & Rutar , A 2022 , ' Local dimensions of self-similar measures satisfying the finite neighbour condition ' , Nonlinearity , vol. 35 , no. 9 , pp. 4876-4904 . https://doi.org/10.1088/1361-6544/ac8040en
dc.identifier.issn0951-7715
dc.identifier.otherORCID: /0000-0001-5173-992X/work/118411791
dc.identifier.urihttps://hdl.handle.net/10023/26035
dc.descriptionKEH was supported by NSERC Grant 2016-03719. AR was supported by this grant as well as EPSRC Grant EP/V520123/1.en
dc.description.abstractWe study sets of local dimensions for self-similar measures in R satisfying the finite neighbour condition, which is formally stronger than the weak separation condition (WSC) but satisfied in all known examples. Under a mild technical assumption, we establish that the set of attainable local dimensions is a finite union of (possibly singleton) compact intervals. The number of intervals is bounded above by the number of non-trivial maximal strongly connected components of a finite directed graph construction depending only on the governing iterated function system. We also explain how our results allow computations of the sets of local dimensions in many explicit cases. This contextualises and generalises a vast amount of prior work on sets of local dimensions for self-similar measures satisfying the WSC.
dc.format.extent29
dc.format.extent948968
dc.language.isoeng
dc.relation.ispartofNonlinearityen
dc.subjectIterated function systemen
dc.subjectSelf-similaren
dc.subjectLocal dimensionen
dc.subjectMultifractal analysisen
dc.subjectWeak separatopm conditionen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectNISen
dc.subject.lccQAen
dc.titleLocal dimensions of self-similar measures satisfying the finite neighbour conditionen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1088/1361-6544/ac8040
dc.description.statusPeer revieweden


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