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Publication - Dr Thomas Jordan

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


    Fraser, J, Jordan, T & Jurga, N, 2018, ‘Dimensions of equilibrium measures on a class of planar self-affine sets’. Journal of Fractal Geometry.


    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.

    Mathematics Subject Classification 2010: primary: 37C45; secondary: 28A80.
    Key words and phrases: self-affine set, K¨aenm¨aki measure, quasi-Bernoulli measure,
    exact dimensional, Ledrappier-Young formula.

    Full details in the University publications repository