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

Robert L. Devaney. "Structure of the McMullen domain in the parameter planes for rational maps." Fundamenta Mathematicae 185.3 (2005): 267-285. <http://eudml.org/doc/283212>.

@article{RobertL2005,
abstract = {We show that, for the family of functions $F_\{λ\}(z) = zⁿ + λ/zⁿ$ 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.},
author = {Robert L. Devaney},
journal = {Fundamenta Mathematicae},
keywords = {Julia set; Cantor set of circles},
language = {eng},
number = {3},
pages = {267-285},
title = {Structure of the McMullen domain in the parameter planes for rational maps},
url = {http://eudml.org/doc/283212},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Robert L. Devaney
TI - Structure of the McMullen domain in the parameter planes for rational maps
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 3
SP - 267
EP - 285
AB - We show that, for the family of functions $F_{λ}(z) = zⁿ + λ/zⁿ$ 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.
LA - eng
KW - Julia set; Cantor set of circles
UR - http://eudml.org/doc/283212
ER -