Hausdorr Dimension and Conformal Dynamics Iii: Computation of Dimension
نویسنده
چکیده
This paper presents an eigenvalue algorithm for accurately computing the Hausdorr dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials and Blaschke products, yielding both numerical and theoretical results. Dimension graphs are presented for (a) the family of Fuchsian groups generated by reeections in 3 symmetric geodesics; (b) the family of polynomials f c (z) = z 2 + c, c 2 ?1; 1=2]; and (c) the family of rational maps f t (z) = z=t + 1=z, t 2 (0; 1]. We also calculate H: dim(() 1:305688 for the Apollonian gasket, and H: dim(J(f)) 1:3934 for Douady's rabbit, where f (z) = z 2 + c satisses f 3 (0) = 0.
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