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Geometric properties
of Julia sets of the composition of polynomials of the form
z2 +
cn
Rainer Brück |
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Vol. 198 (2001), No. 2, 347–372
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Abstract |
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For a sequence (cn) of complex numbers we consider the quadratic polynomials fcn(z) := z2 + cn and the sequence (Fn) of iterates Fn := fcn ∘⋯∘fc1. The Fatou set ℱ(cn) is by definition the set of all z ∈ℂ such that (Fn) is normal in some neighbourhood of z, while the complement of ℱ(cn) is called the Julia set 𝒥(cn). The aim of this article is to study geometric properties, Lebesgue measure and Hausdorff dimension of the Julia set 𝒥(cn) provided that the sequence (cn) is bounded. |
Milestones
Received: 16 June 1999
Revised: 20 September 1999
Published: 1 April 2001
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Authors |
| Rainer Brück | |
| Justus-Liebig-Universität
Gießen Arndtstraße 2 35392 Gießen Germany |
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