The Hausdorff dimension of quasi-circles: a result of Ruelle and Bowen

Abstract

We provide an expanded and clarified proof of the famous result of Bowen and Ruelle giving an asymptotic formula for the Hausdorff dimension of quasi-circles corresponding to the Julia sets of $f(z)=z^2+c$ for small $c$. The proof does not contain new material but has been rewritten to make it more accessible to MSc or PhD students with an interest in dimension theory.

9 pages, 2 figures, to be submitted to The American Mathematical Monthly