Files in this item
Lq-spectra of self-affine measures : closed forms, counterexamples, and split binomial sums
Item metadata
dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Lee, Lawrence D. | |
dc.contributor.author | Morris, Ian D. | |
dc.contributor.author | Yu, Han | |
dc.date.accessioned | 2021-09-23T16:30:07Z | |
dc.date.available | 2021-09-23T16:30:07Z | |
dc.date.issued | 2021-09 | |
dc.identifier | 275857691 | |
dc.identifier | 310ceaa0-60ff-4bf5-adc0-7018b94670fa | |
dc.identifier | 85113411228 | |
dc.identifier | 000680669200001 | |
dc.identifier.citation | Fraser , 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 . https://doi.org/10.1088/1361-6544/ac14a2 | en |
dc.identifier.issn | 0951-7715 | |
dc.identifier.other | RIS: urn:15BEA95C3B10CCD86173B3E01899CF3F | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/100172576 | |
dc.identifier.uri | https://hdl.handle.net/10023/24017 | |
dc.description | Funding: 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.abstract | We 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.format.extent | 27 | |
dc.format.extent | 921991 | |
dc.language.iso | eng | |
dc.relation.ispartof | Nonlinearity | en |
dc.subject | Fractals | en |
dc.subject | Lq-spectra | en |
dc.subject | Self-affine measures | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Lq-spectra of self-affine measures : closed forms, counterexamples, and split binomial sums | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1088/1361-6544/ac14a2 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2016-500 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.