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dc.contributor.authorFraser, Jonathan MacDonald
dc.contributor.authorJordan, Thomas
dc.contributor.authorJurga, Natalia
dc.identifier.citationFraser , J M , Jordan , T & Jurga , N 2020 , ' Dimensions of equilibrium measures on a class of planar self-affine sets ' , Journal of Fractal Geometry , vol. 7 , no. 1 , pp. 87–111 .
dc.identifier.otherPURE: 256234555
dc.identifier.otherPURE UUID: 6fa0414e-023a-4a6d-86be-fc46c0b307d7
dc.identifier.otherWOS: 000548154400003
dc.identifier.otherORCID: /0000-0002-8066-9120/work/79917925
dc.identifier.otherScopus: 85090839399
dc.descriptionFunding: JMF was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500).en
dc.description.abstractWe study equilibrium measures (Käenmäki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property. Our main result is that such measures are exact dimensional and the dimension satisfies the Ledrappier–Young formula, which gives an explicit expression for the dimension in terms of the entropy and Lyapunov exponents as well as the dimension of a coordinate projection of the measure. In particular, we do this by showing that the Käenmäki measure is equal to the sum of (the pushforwards) of two Gibbs measures on an associated subshift of finite type.
dc.relation.ispartofJournal of Fractal Geometryen
dc.rights© 2018, European Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectSelf-affine seten
dc.subjectKäenmäki measureen
dc.subjectQuasi-Bernoulli measureen
dc.subjectExact dimensionalen
dc.subjectLedrappier-Young formulaen
dc.subjectQA Mathematicsen
dc.titleDimensions of equilibrium measures on a class of planar self-affine setsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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