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dc.contributor.authorFraser, JM
dc.contributor.authorLee, LD
dc.contributor.authorMorris, ID
dc.contributor.authorYu, Han
dc.date.accessioned2022-01-05T16:34:37Z
dc.date.available2022-01-05T16:34:37Z
dc.date.issued2021-09
dc.date.submitted2020-09-14
dc.identifier.issn0951-7715
dc.identifier.othernonac14a2
dc.identifier.otherac14a2
dc.identifier.othernon-104844.r1
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/332100
dc.description.abstract<jats:title>Abstract</jats:title> <jats:p>We study <jats:italic>L</jats:italic> <jats:sup> <jats:italic>q</jats:italic> </jats:sup>-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 <jats:italic>L</jats:italic> <jats:sup> <jats:italic>q</jats:italic> </jats:sup>-spectrum. As a further application we provide examples of self-affine measures whose <jats:italic>L</jats:italic> <jats:sup> <jats:italic>q</jats:italic> </jats:sup>-spectra exhibit new types of phase transitions. Finally, we provide new non-trivial closed form bounds for the <jats:italic>L</jats:italic> <jats:sup> <jats:italic>q</jats:italic> </jats:sup>-spectra, which in certain cases yield sharp results.</jats:p>
dc.languageen
dc.publisherIOP Publishing
dc.subjectPaper
dc.subjectfractals
dc.subjectself-affine measures
dc.subjectL q -spectra
dc.subject2010: primary: 28A80
dc.subject37C45
dc.subjectsecondary: 15A18
dc.subject26A24
dc.titleL<sup>q</sup>-spectra of self-affine measures: Closed forms, counterexamples, and split binomial sums
dc.typeArticle
dc.date.updated2022-01-05T16:34:36Z
prism.endingPage6357
prism.issueIdentifier9
prism.publicationNameNonlinearity
prism.startingPage6331
prism.volume34
dc.identifier.doi10.17863/CAM.79547
dcterms.dateAccepted2021-07-14
rioxxterms.versionofrecord10.1088/1361-6544/ac14a2
rioxxterms.versionVoR
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/3.0/
dc.contributor.orcidFraser, JM [0000-0002-8066-9120]
dc.identifier.eissn1361-6544
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/N509759/1, EP/R015104/1)
pubs.funder-project-idLeverhulme Trust (RF-2016-500, RPG-2016-194)
cam.issuedOnline2021-08-02


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