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Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets

Oliver Jenkinson and Mark Pollicott
American Journal of Mathematics
Vol. 124, No. 3 (Jun., 2002), pp. 495-545
Stable URL: http://www.jstor.org/stable/25099125
Page Count: 51
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Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets
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Abstract

We present a new algorithm for efficiently computing the Hausdorff dimension of sets X invariant under conformal expanding dynamical systems. By locating the periodic points of period up to N, we construct approximations $s_{N}$ which converge to dim(X) super-exponentially fast in N. This method can be used to give rigorous estimates for important examples, including hyperbolic Julia sets and limit sets of Schottky and quasifuchsian groups.

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