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The Assouad dimension of self-affine measures on sponges
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Kolossvary, Istvan Tamas | |
dc.date.accessioned | 2022-09-12T12:30:01Z | |
dc.date.available | 2022-09-12T12:30:01Z | |
dc.date.issued | 2022-09-08 | |
dc.identifier.citation | Fraser , 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.2022.64 | en |
dc.identifier.issn | 0143-3857 | |
dc.identifier.other | PURE: 280848703 | |
dc.identifier.other | PURE UUID: c2919de9-f96c-462e-a4a9-876a616fc8f1 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/119212583 | |
dc.identifier.other | ORCID: /0000-0002-2216-305X/work/119212746 | |
dc.identifier.other | WOS: 000851333100001 | |
dc.identifier.other | Scopus: 85152544424 | |
dc.identifier.uri | https://hdl.handle.net/10023/25993 | |
dc.description | Funding: Royal Society of Edinburgh - 70249; Leverhulme Trust - RPG-2019-034; Engineering and Physical Sciences Research Council - EP/R015104/1. | en |
dc.description.abstract | We 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.extent | 23 | |
dc.language.iso | eng | |
dc.relation.ispartof | Ergodic Theory and Dynamical Systems | en |
dc.rights | Copyright © 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.subject | Assouad dimension | en |
dc.subject | Lower dimension | en |
dc.subject | Self-affine carpet | en |
dc.subject | Self-affine sponge | en |
dc.subject | Dimension gap | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | The Assouad dimension of self-affine measures on sponges | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1017/etds.2022.64 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
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