Title: Variation of Hausdorff dimension of Julia sets
Abstract: Abstract Let ( R λ ) λ∈ D be an analytic family of rational maps of degree d ≥ 2, where D is a simply connected domain in ℂ, and each R λ is hyperbolic. Then the Hausdorff dimension δ(λ) of the Julia set of R λ satisfies where ℋ is a collection of harmonic functions u on D . We examine some consequences of this, and show how it can be used to obtain estimates for the Hausdorff dimension of some particular Julia sets.
Publication Year: 1993
Publication Date: 1993-03-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 13
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