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 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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 495-545
Launched on MUSE
2002-06-01
Open Access
No
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