Dimensions of equilibrium measures on a class of planar self-affine sets
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We 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.
Fraser , 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 . https://doi.org/10.4171/JFG/85
Journal of Fractal Geometry
© 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 https://doi.org/10.4171/JFG/85
DescriptionFunding: JMF was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500).
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