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EXPLICIT RATIONAL FUNCTIONS WHOSE JULIA SETS ARE JORDAN ARCS

Published online by Cambridge University Press:  24 May 2004

CLEMENS INNINGER  and
FRANZ PEHERSTORFER
CLEMENS INNINGER
Affiliation:
Institut für Analysis, Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austriafranz.peherstorfer@jku.atclemensinninger@hotmail.com
FRANZ PEHERSTORFER
Affiliation:
Institut für Analysis, Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austriafranz.peherstorfer@jku.atclemensinninger@hotmail.com
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Abstract

A class of rational functions and sufficient conditions on it such that the Julia set is a Jordan arc, respectively no Jordan arc, are introduced. Further, it is shown that any rational function which has a Jordan arc as Julia set belongs up to Möbius conjugation to this class.

Keywords

37F1030D0526C1539B12
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 676 - 692
Copyright
The London Mathematical Society 2004

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Footnotes

This work was supported by the Austrian Science Fund FWF, projects P12985-TEC and P16390-N04.