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Generalised dimensions of measures on almost self-affine sets

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Preprint
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DOI: 10.1088/0951-7715/23/5/002
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arXiv
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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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