Structure of the McMullen domain in the parameter planes for rational maps

Robert L. Devaney

Fundamenta Mathematicae, Tome 185 (2005), p. 267-285 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that, for the family of functions $F_{λ} (z) = z ⁿ + λ / z ⁿ$ where n ≥ 3 and λ ∈ ℂ, there is a unique McMullen domain in parameter space. A McMullen domain is a region where the Julia set of $F_{λ}$ is homeomorphic to a Cantor set of circles. We also prove that this McMullen domain is a simply connected region in the plane that is bounded by a simple closed curve.

Publié le : 2005-01-01

Zbl 1093.37016

EUDML-ID : urn:eudml:doc:283212

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     title = {Structure of the McMullen domain in the parameter planes for rational maps},
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     year = {2005},
     pages = {267-285},
     zbl = {1093.37016},
     language = {en},
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Robert L. Devaney. Structure of the McMullen domain in the parameter planes for rational maps. Fundamenta Mathematicae, Tome 185 (2005) pp. 267-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-5/