Geodesic
Structure of the McMullen domain in the parameter planes for rational maps
Robert L. Devaney1
1 Boston University Boston, MA 02215, U.S.A.
Fundamenta Mathematicae, Tome 185 (2005) no. 3, pp. 267-285

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that, for the family of functions $ F_\lambda(z) = z^n + {\lambda\over z^n} $ where $n \geq 3$ and $\lambda \in {\mathbb C}$, there is a unique McMullen domain in parameter space. A McMullen domain is a region where the Julia set of $F_\lambda$ 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.
DOI : 10.4064/fm185-3-5
Keywords: family functions lambda lambda where geq lambda mathbb there unique mcmullen domain parameter space mcmullen domain region where julia set lambda homeomorphic cantor set circles prove mcmullen domain simply connected region plane bounded simple closed curve

Robert L. Devaney 1

1 Boston University Boston, MA 02215, U.S.A. 
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Robert L. Devaney. Structure of the McMullen domain
in the parameter planes for rational maps. Fundamenta Mathematicae, Tome 185 (2005) no. 3, pp. 267-285. doi: 10.4064/fm185-3-5

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