Generalised dimensions of measures on almost self-affine sets

Details Generalised dimensions of measures on almost self-affine sets Generalised dimensions of measures on almost self-affine sets

2009-11-04

arxiv.org/abs/0911.0744v1

Mathematics

Metric Geometry

Scientific paper

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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