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arXiv · 1509.07558

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

Catherine Bruce
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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.

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Catherine Bruce. 2015-09-24. The Hausdorff dimension of quasi-circles: a result of Ruelle and Bowen. https://arxiv.org/abs/1509.07558

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