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arXiv · 0911.0744

Generalised dimensions of measures on almost self-affine sets

K. J. Falconer
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Abstract

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees.

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K. J. Falconer. 2009-11-04. Generalised dimensions of measures on almost self-affine sets. https://doi.org/10.1088/0951-7715%2F23%2F5%2F002

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