On the frequency of partial quotients of regular continued fractions

Abstract

We consider sets of real numbers in $[0,1)$ with prescribed frequencies of partial quotients in their regular continued fraction expansions. It is shown that the Hausdorff dimensions of these sets, always bounded from below by $1/2$, are given by a modified variational principle.

Accepted by Mathematical Proceedings of the Cambridge Philosophical Society

Cited by in corpus (2)

• Multifractal analysis of Birkhoff averages for countable Markov maps
• Multifractal analysis for Markov interval maps with countably many branches