Dimension of contracting on average self-similar measures

Abstract

We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all scales is sufficient. Our proof uses a technique we call the variance summation method, avoiding the use of inverse theorems for entropy.

arXiv comment26 pages. arXiv admin note: text overlap with arXiv:2409.18936