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CONNECTEDNESS AND STABILITY OF JULIA SETS OF THE COMPOSITION OF POLYNOMIALS OF THE FORM z2+cn

Published online by Cambridge University Press:  01 April 2000

RAINER BRÜCK
RAINER BRÜCK
Affiliation:
Mathematisches Institut, Justus-Liebig-Universität Giessen, Arndtstrasse 2, D-35392 Giessen, Germany Current address: Fachbereich 7 - Mathematik, Bergische Universität - Gesamthochschule Wuppertal, Gaussstrasse 20, D-42097 Wuppertal, Germany; [email protected]
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Abstract

For a sequence (cn) of complex numbers, the quadratic polynomials fcn(z) := z2 + cn and the sequence (Fn) of iterates Fn := fcn∘…∘fc1 are considered. The Fatou set [Fscr ](cn) is by definition the set of all z ∈ [Copf ]ˆ such that (Fn) is normal in some neighbourhood of z, while the complement of [Fscr ](cn) is called the Julia set [Jscr ](cn). The aim of this article is to study the connectedness and stability of the Julia set [Jscr ](cn) provided that the sequence (cn) is bounded.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 462 - 470
Copyright
The London Mathematical Society 2000

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