Self-similar sets and measures on the line

Abstract

We discuss the problem of determining the dimension of self-similar sets and measures on $\mathbf{R}$. We focus on the developments of the last four years. At the end of the paper, we survey recent results about other aspects of self-similar measures including their Fourier decay and absolute continuity.

28 pages

References in corpus (2)

• Self-similar sets with super-exponential close cylinders
• On the Rajchman property for self-similar measures on ${\mathbb{R}}^d$

Cited by in corpus (1)

• Towards Absolutely Continuous Bernoulli Convolutions