A global Boettcher's theorem

We prove a global result for rational functions that is analogous to a local theorem of L. E. Boettcher (1904). Under the hypotheses that f is a complex rational function with a superattractive fixed point α of order $p \ge 2$ and that α is the only critical point of f in the immediate basin of attraction of α, we prove that there exists a conformal map $w = \varphi(z)$ of the entire immediate basin of attraction of α onto the unit disk such that $(\varphi \circ f \circ \varphi\sp{-1})(w) = w\sp{p}.$

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kline, Bradford J.

Contributors dc:contributor

• Miles, Joseph B.

• Mathematics

Statement dc:rights

• Copyright 1995 Kline, Bradford J.

Language dc:language

eng

Identifier

AAI9543631
(UMI)AAI9543631

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21910