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dc.contributor.authorHare, Kathryn
dc.contributor.authorRutar, Alex
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 .
dc.identifier.otherPURE: 281147528
dc.identifier.otherPURE UUID: b4c69f18-e830-4ce2-bae2-4890582f5909
dc.identifier.otherORCID: /0000-0001-5173-992X/work/118411791
dc.identifier.otherScopus: 85137241538
dc.identifier.otherWOS: 000842713100001
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.rightsCopyright © 2022 IOP Publishing Ltd & London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.en
dc.subjectIterated function systemen
dc.subjectLocal dimensionen
dc.subjectMultifractal analysisen
dc.subjectWeak separatopm conditionen
dc.subjectQA Mathematicsen
dc.titleLocal dimensions of self-similar measures satisfying the finite neighbour conditionen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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