arXiv:1509.07558 Abstract | arXiv Analytics

arXiv:1509.07558 [math.DS]Abstract References Reviews Resources

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

Published 2015-09-24Version 1

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.

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

Categories: math.DS

Subjects: 37C45, 28A80, 37F50

Keywords: hausdorff dimension, quasi-circles, asymptotic formula, dimension theory, julia sets

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