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dc.contributor.authorFraser, Jonathan
dc.contributor.authorKolossvary, Istvan Tamas
dc.date.accessioned2022-09-12T12:30:01Z
dc.date.available2022-09-12T12:30:01Z
dc.date.issued2022-09-08
dc.identifier.citationFraser , J & Kolossvary , I T 2022 , ' The Assouad dimension of self-affine measures on sponges ' , Ergodic Theory and Dynamical Systems , vol. FirstView . https://doi.org/10.1017/etds.2022.64en
dc.identifier.issn0143-3857
dc.identifier.otherPURE: 280848703
dc.identifier.otherPURE UUID: c2919de9-f96c-462e-a4a9-876a616fc8f1
dc.identifier.otherORCID: /0000-0002-8066-9120/work/119212583
dc.identifier.otherORCID: /0000-0002-2216-305X/work/119212746
dc.identifier.otherWOS: 000851333100001
dc.identifier.otherScopus: 85152544424
dc.identifier.urihttps://hdl.handle.net/10023/25993
dc.descriptionFunding: Royal Society of Edinburgh - 70249; Leverhulme Trust - RPG-2019-034; Engineering and Physical Sciences Research Council - EP/R015104/1.en
dc.description.abstractWe derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in ℝd generated by diagonal matrices and satisfying suitable separation conditions. The upper and lower bounds always coincide for d=2,3 , yielding precise explicit formulae for those dimensions. Moreover, there are easy-to-check conditions guaranteeing that the bounds coincide for d⩾4 . An interesting consequence of our results is that there can be a ‘dimension gap’ for such self-affine constructions, even in the plane. That is, we show that for some self-affine carpets of ‘Barański type’ the Assouad dimension of all associated self-affine measures strictly exceeds the Assouad dimension of the carpet by some fixed δ>0 depending only on the carpet. We also provide examples of self-affine carpets of ‘Barański type’ where there is no dimension gap and in fact the Assouad dimension of the carpet is equal to the Assouad dimension of a carefully chosen self-affine measure.
dc.format.extent23
dc.language.isoeng
dc.relation.ispartofErgodic Theory and Dynamical Systemsen
dc.rightsCopyright © The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.en
dc.subjectAssouad dimensionen
dc.subjectLower dimensionen
dc.subjectSelf-affine carpeten
dc.subjectSelf-affine spongeen
dc.subjectDimension gapen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleThe Assouad dimension of self-affine measures on spongesen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.sponsorEPSRCen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/etds.2022.64
dc.description.statusPeer revieweden
dc.identifier.grantnumberRPG-2019-034en
dc.identifier.grantnumberEP/R015104/1en


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