Connectedness and Stability of Julia Sets of the Composition of Polynomials of the Form z2+cn |
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| Authors: | Bruck Rainer |
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| Affiliation: | Mathematisches Institut, Justus-Liebig-Universität Giessen Arndtstrasse 2, D-35392 Giessen, Germany |
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| Abstract: | For a sequence (cn) of complex numbers, the quadratic polynomialsfcn(z) := z2 + cn and the sequence (Fn) of iterates Fn := fcn ...fc1areconsidered. The Fatou set F(cn) is by definition the set ofall z  C^ such that (Fn) is normal in some neighbourhood ofz, while the complement of F(cn) is called the Julia set J(cn).The aim of this article is to study the connectedness and stabilityof the Julia set J(cn) provided that the sequence (cn) is bounded. |
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