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Journal of the London Mathematical Society 2004 69(3):676-692; doi:10.1112/S0024610704005204
© 2004 by London Mathematical Society
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© The London Mathematical Society

Explicit Rational Functions Whose Julia Sets are Jordan Arcs

Clemens Inninger and Franz Peherstorfer

Institut für Analysis, Universität Linz Altenbergerstrasse 69, 4040 Linz, Austria, clemensinninger{at}hotmail.com
Institut für Analysis, Universität Linz Altenbergerstrasse 69, 4040 Linz, Austria, franz.peherstorfer{at}jku.at

Received 4 February 2002. Revision received 27 August 2003.

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.


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