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arXiv · 1908.00271

Dimension of ergodic measures projected onto self-similar sets with overlaps

Thomas Jordan·Ariel Rapaport
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Abstract

For self-similar sets on $\mathbb{R}$ satisfying the exponential separation condition we show that the natural projections of shift invariant ergodic measures is equal to $\min\{1,\frac{h}{-\chi}\}$, where $h$ and $\chi$ are the entropy and Lyapunov exponent respectively. The proof relies on Shmerkin's recent result on the $L^{q}$ dimension of self-similar measures. We also use the same method to give results on convolutions and orthogonal projections of ergodic measures projected onto self-similar sets.

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Thomas Jordan, Ariel Rapaport. 2019-08-01. Dimension of ergodic measures projected onto self-similar sets with overlaps. https://doi.org/10.1112/plms.12337

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