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Variation of Hausdorff dimension of Julia sets
Published online by Cambridge University Press: 19 September 2008
Abstract
Let (Rλ)λ∈D be an analytic family of rational maps of degree d ≥ 2, where D is a simply connected domain in ℂ, and each Rλ is hyperbolic. Then the Hausdorff dimension δ(λ) of the Julia set of Rλ 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.
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