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arXiv · 2501.17795

Dimension of contracting on average self-similar measures

Samuel Kittle·Constantin Kogler
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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.

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Samuel Kittle, Constantin Kogler. 2025-01-29. Dimension of contracting on average self-similar measures. https://arxiv.org/abs/2501.17795

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