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Computational Methods and Function Theory 7 (2007), No. 2, 415--427
Copyright Heldermann Verlag 2007

Rational Maps with Fatou Components of Arbitrary Connectivity Number

Marcus Stiemer
stiemer@math.uni-dortmund.de , Universität Dortmund, Fachbereich Mathematik, 44221 Dortmund, Germany.

[Abstract-pdf] [Abstract-ps]

Periodic components of the Fatou set of a rational map are either simply, doubly or infinitely connected. However, preimages of these may possibly possess a higher finite connectivity. The purpose of this article is to study certain classes of generalized Blaschke products that possess Fatou components of a given arbitrary finite connectivity number.

Keywords: Iteration of rational functions, Fatou set, complex dynamical systems.

MSC 2000: 37F10, 30D05.

[FullText-pdf (723 K)] [FullText-ps (10551 K)]