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Calculating Hausdorff dimension of Julia sets and Kleinian limit sets

From: American Journal of Mathematics
Volume 124, Number 3, June 2002
pp. 495-545 | 10.1353/ajm.2002.0015



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 sN 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.