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Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

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dc.contributor.authorBoore, Graeme
dc.contributor.authorFalconer, Kenneth John
dc.date.accessioned2012-11-06T14:31:01Z
dc.date.available2012-11-06T14:31:01Z
dc.date.issued2013
dc.identifier.citationBoore , G & Falconer , K J 2013 , ' Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. 154 , no. 02 , pp. 325-349 . https://doi.org/10.1017/S0305004112000576en
dc.identifier.issn0305-0041
dc.identifier.otherPURE: 12209594
dc.identifier.otherPURE UUID: 333aef7d-bf33-4580-8d7f-ae9a9592802b
dc.identifier.otherScopus: 84873551920
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055243
dc.identifier.urihttps://hdl.handle.net/10023/3237
dc.description"GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"en
dc.description.abstractFor directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.
dc.format.extent24
dc.language.isoeng
dc.relation.ispartofMathematical Proceedings of the Cambridge Philosophical Societyen
dc.rightsThis is an author version of this article. The published version (c) Cambridge Philosophical Society 2012 is available at http://journals.cambridge.orgen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleAttractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measureen
dc.typeJournal articleen
dc.description.versionPreprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/S0305004112000576
dc.description.statusPeer revieweden
dc.identifier.urlhttp://journals.cambridge.org/abstract_S0305004112000576en
dc.identifier.urlhttp://arxiv.org/pdf/1108.2418.pdfen


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