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dc.contributor.authorBárány, Balázs
dc.contributor.authorKäenmäki, Antti
dc.contributor.authorKoivusalo, Henna
dc.date.accessioned2019-01-04T06:25:26Z
dc.date.available2019-01-04T06:25:26Z
dc.date.issued2018
dc.identifier.citationBárány, B., Käenmäki, A., & Koivusalo, H. (2018). Dimension of self-affine sets for fixed translation vectors. <i>Journal of the London Mathematical Society</i>, <i>98</i>(1), 223-252. <a href="https://doi.org/10.1112/jlms.12132" target="_blank">https://doi.org/10.1112/jlms.12132</a>
dc.identifier.otherCONVID_28024893
dc.identifier.otherTUTKAID_77490
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/60877
dc.description.abstractAn affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently verified for affine iterated function systems by Bárány and Käenmäki, and a new transversality condition, and in particular they do not depend on properties of the Furstenberg measure. This allows our results to hold for self-affine sets and measures in any Euclidean space.fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherOxford University Press
dc.relation.ispartofseriesJournal of the London Mathematical Society
dc.rightsIn Copyright
dc.subject.othervektorit
dc.subject.othervectors
dc.titleDimension of self-affine sets for fixed translation vectors
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201812175156
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2018-12-17T10:15:22Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange223-252
dc.relation.issn0024-6107
dc.relation.numberinseries1
dc.relation.volume98
dc.type.versionacceptedVersion
dc.rights.copyright© 2018 London Mathematical Society
dc.rights.accesslevelopenAccessfi
dc.subject.ysomatematiikka
dc.subject.ysomatemaattiset käsitteet
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
jyx.subject.urihttp://www.yso.fi/onto/yso/p27190
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1112/jlms.12132


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