Multi-scale properties of continued fraction sets

Abstract

We survey the dimension theory of sets of real numbers with regular continued fraction expansion restricted to a non-empty and possibly infinite subset $\mathcal{D}\subset \mathbb{N}$.

33 pages, 2 figures. Overview article based on arXiv:2406.12821 prepared for minicourse at the Simons semester on continued fractions at IMPAN, Warsaw, in 2026