# Self-similar measures associated to a homogeneous system of three maps

@article{Rapaport2020SelfsimilarMA, title={Self-similar measures associated to a homogeneous system of three maps}, author={Ariel Rapaport and P'eter P'al Varj'u}, journal={arXiv: Dynamical Systems}, year={2020} }

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and Barany, Kaenmaki. To overcome the difficulties stemming form these, we develop novel techniques, including an…

## 4 Citations

### Estimates on the dimension of self‐similar measures with overlaps

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### Self-similar sets and measures on the line

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- 2021

We discuss the problem of determining the dimension of self-similar sets and measures on R. We focus on the developments of the last four years. At the end of the paper, we survey recent results…

### Pointwise normality and Fourier decay for self-conformal measures

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