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Dimensions of equilibrium measures on a class of planar self-affine sets

Fraser, Jonathan M, Jordan, Thomas and Jurga, Natalia (2018) Dimensions of equilibrium measures on a class of planar self-affine sets Journal of Fractal Geometry.

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We study equilibrium measures (K ̈aenm ̈aki 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 K ̈aenm ̈aki measure is equal to the sum of (the pushforwards) of two Gibbs measures on an associated subshift of finite type.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Fraser, Jonathan M
Jordan, Thomas
Date : 2018
Copyright Disclaimer : Copyright 2018 European Mathematical Society
Uncontrolled Keywords : self-affine set, K ̈aenm ̈aki measure, quasi-Bernoulli mea- sure, exact dimensional, Ledrappier-Young formula
Depositing User : Melanie Hughes
Date Deposited : 20 Sep 2018 13:42
Last Modified : 19 Oct 2018 09:11

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