Generalised dimensions of measures on almost self-affine sets
Metric Geometry
2015-05-14 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.0911.0744,
title = {Generalised dimensions of measures on almost self-affine sets},
author = {K. J. Falconer},
journal= {arXiv preprint arXiv:0911.0744},
year = {2015}
}