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dc.contributor.authorFraser, Jonathan
dc.contributor.authorLee, Lawrence D.
dc.contributor.authorMorris, Ian D.
dc.contributor.authorYu, Han
dc.identifier.citationFraser , J , Lee , L D , Morris , I D & Yu , H 2021 , ' L q -spectra of self-affine measures : closed forms, counterexamples, and split binomial sums ' , Nonlinearity , vol. 34 , no. 9 , pp. 6331-6357 .
dc.identifier.otherPURE: 275857691
dc.identifier.otherPURE UUID: 310ceaa0-60ff-4bf5-adc0-7018b94670fa
dc.identifier.otherRIS: urn:15BEA95C3B10CCD86173B3E01899CF3F
dc.identifier.otherScopus: 85113411228
dc.identifier.otherORCID: /0000-0002-8066-9120/work/100172576
dc.identifier.otherWOS: 000680669200001
dc.descriptionFunding: Jonathan Fraser was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1). Lawrence Lee was supported by an EPSRC Doctoral Training Grant (EP/N509759/1). Ian Morris was supported by a Leverhulme Trust Research Project Grant (RPG-2016-194). Han Yu was financially supported by the University of St Andrews.en
dc.description.abstractWe study Lq-spectra of planar self-affine measures generated by diagonal matrices. We introduce a new technique for constructing and understanding examples based on combinatorial estimates for the exponential growth of certain split binomial sums. Using this approach we disprove a theorem of Falconer and Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of generic self-affine measures. We also answer a question of Fraser from 2016 in the negative by proving that a certain natural closed form expression does not generally give the Lq-spectrum. As a further application we provide examples of self-affine measures whose Lq-spectra exhibit new types of phase transitions. Finally, we provide new nontrivial closed form bounds for the Lq-spectra, which in certain cases yield sharp results.
dc.rightsCopyright © 2021 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.subjectSelf-affine measuresen
dc.subjectQA Mathematicsen
dc.titleLq-spectra of self-affine measures : closed forms, counterexamples, and split binomial sumsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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