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Dimension spectrum of infinite self-affine iterated function systems

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dc.contributor.authorJurga, Natalia Anna
dc.date.accessioned2021-07-05T15:30:10Z
dc.date.available2021-07-05T15:30:10Z
dc.date.issued2021-06-16
dc.identifier.citationJurga , N A 2021 , ' Dimension spectrum of infinite self-affine iterated function systems ' , Selecta Mathematica: New Series , vol. 27 , no. 3 , 49 . https://doi.org/10.1007/s00029-021-00674-xen
dc.identifier.issn1420-9020
dc.identifier.otherPURE: 274570657
dc.identifier.otherPURE UUID: a11c2277-0786-41ba-b99a-e2ac000fe83c
dc.identifier.otherScopus: 85108167030
dc.identifier.otherWOS: 000691146600001
dc.identifier.urihttps://hdl.handle.net/10023/23473
dc.descriptionFunding: The author was financially supported by the Leverhulme Trust (Research Project Grant number RPG-2016-194) and by the EPSRC (Standard Grant EP/R015104/1).en
dc.description.abstractGiven an infinite iterated function system (IFS) F, we define its dimension spectrum D(F) to be the set of real numbers which can be realised as the dimension of some subsystem of F. In the case where FF is a conformal IFS, the properties of the dimension spectrum have been studied by several authors. In this paper we investigate for the first time the properties of the dimension spectrum when F is a non-conformal IFS. In particular, unlike dimension spectra of conformal IFS which are always compact and perfect (by a result of Chousionis, Leykekhman and Urbański, Selecta 2019), we construct examples to show that D(F) need not be compact and may contain isolated points.
dc.format.extent23
dc.language.isoeng
dc.relation.ispartofSelecta Mathematica: New Seriesen
dc.rightsCopyright © The Author(s) 2021. 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.en
dc.subjectIterated function systemen
dc.subjectSelf-affline seten
dc.subjectDimension spectrumen
dc.subjectHausdorff dimensionen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleDimension spectrum of infinite self-affine iterated function systemsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s00029-021-00674-x
dc.description.statusPeer revieweden
dc.identifier.grantnumberEP/R015104/1en


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