Hausdorff dimension and conformal dynamics, III: Computation of dimension
نویسندگان
چکیده
منابع مشابه
Hausdorff dimension and conformal dynamics III: Computation of dimension
This paper presents an eigenvalue algorithm for accurately computing the Hausdorff 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 reflections in 3 ...
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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 sy...
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This paper investigates several dynamically defined dimensions for rational maps f on the Riemann sphere, providing a systematic treatment modeled on the theory for Kleinian groups. We begin by defining the radial Julia set Jrad(f), and showing that every rational map satisfies H. dimJrad(f) = α(f) where α(f) is the minimal dimension of an f -invariant conformal density on the sphere. A rationa...
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1.1. Statement of the results. One of the first questions usually asked about a fractal subset of R is whether it has the maximal possible Hausdorff dimension, n. It certainly happens if the set has positive Lebesgue measure. On the other hand, it is easy to construct fractal sets of zero measure but of dimension n. Moreover, this phenomenon is often observable for fractal sets produced by conf...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1998
ISSN: 1080-6377
DOI: 10.1353/ajm.1998.0031