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Dyadic approximation in the middle-third Cantor set

dc.contributor.authorAllen, D
dc.contributor.authorChow, S
dc.contributor.authorYu, H
dc.date.accessioned2022-10-03T11:02:23Z
dc.date.issued2022-11-29
dc.date.updated2022-10-03T10:10:33Z
dc.description.abstractIn this paper, we study the metric theory of dyadic approximation in the middle-third Cantor set. This theory complements earlier work of Levesley et al. (Math Ann 338(1):97–118, 2007), who investigated the problem of approximation in the Cantor set by triadic rationals. We find that the behaviour when we consider dyadic approximation in the Cantor set is substantially different to considering triadic approximation in the Cantor set. In some sense, this difference in behaviour is a manifestation of Furstenberg’s times 2 times 3 phenomenon from dynamical systems, which asserts that the base 2 and base 3 expansions of a number are not both structured.en_GB
dc.description.sponsorshipHeilbronn Institute for Mathematical Researchen_GB
dc.description.sponsorshipEngineering and Physical Sciences Research Council (EPSRC)en_GB
dc.description.sponsorshipSwedish Research Councilen_GB
dc.description.sponsorshipEuropean Union Horizon 2020en_GB
dc.identifier.citationVol. 29, article 11en_GB
dc.identifier.doi10.1007/s00029-022-00814-x
dc.identifier.grantnumberEP/S00226X/2en_GB
dc.identifier.grantnumber2016-06596en_GB
dc.identifier.grantnumber803711en_GB
dc.identifier.urihttp://hdl.handle.net/10871/131068
dc.identifierORCID: 0000-0002-1778-7183 (Allen, Demi)
dc.language.isoenen_GB
dc.publisherSpringer / Birkhäuser Verlagen_GB
dc.rights© The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
dc.subjectDiophantine approximationen_GB
dc.subjectmiddle-third Cantor seten_GB
dc.subjectHausdorff measuresen_GB
dc.subjectFourier analysisen_GB
dc.subject×2 × 3 phenomenonen_GB
dc.titleDyadic approximation in the middle-third Cantor seten_GB
dc.typeArticleen_GB
dc.date.available2022-10-03T11:02:23Z
dc.identifier.issn1420-9020
dc.descriptionThis is the final version. Available on open access from Springer via the DOI in this recorden_GB
dc.identifier.journalSelecta Mathematica, New Seriesen_GB
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_GB
dcterms.dateAccepted2022-09-28
dcterms.dateSubmitted2021-09-13
rioxxterms.versionVoRen_GB
rioxxterms.licenseref.startdate2022-09-28
rioxxterms.typeJournal Article/Reviewen_GB
refterms.dateFCD2022-10-03T10:10:37Z
refterms.versionFCDAM
refterms.dateFOA2022-12-19T14:08:51Z
refterms.panelBen_GB


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© The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Except where otherwise noted, this item's licence is described as © The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.