Dimension of contracting on average self-similar measures
Dynamical Systems
2025-01-30 v1 Classical Analysis and ODEs
Probability
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.
Keywords
Cite
@article{arxiv.2501.17795,
title = {Dimension of contracting on average self-similar measures},
author = {Samuel Kittle and Constantin Kogler},
journal= {arXiv preprint arXiv:2501.17795},
year = {2025}
}
Comments
26 pages. arXiv admin note: text overlap with arXiv:2409.18936