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File:Julia set of a hyperbolic entire function in the Laguerre-Polya class Square.svg

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English: This is a high-resolution version of Figure 1(b) from the paper "Hyperbolic entire functions with bounded Fatou components" by Bergweiler, Fagella and Rempe-Gillen (https://arxiv.org/abs/1404.0925). The Julia set is shown in black. The map is . Here there are superattracting fixed points at 0 and -1 (marked with filled circles), and 0 is an asymptotic value. The basin of 0 is coloured white and the basin of -1 is coloured grey. Every Fatou component is a Jordan domain, but all pre-periodic components of the basin of 0 are unbounded, and the Julia set is not locally connected. The non-periodic critical point 1 is marked by asterisks.
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Source This file was derived from: Julia set of a hyperbolic entire function in the Laguerre-Polya class.svg: 
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This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: zum Quadrat angepasst. The original can be viewed here: Julia set of a hyperbolic entire function in the Laguerre-Polya class.svg: . Modifications made by Yomomo.

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current21:02, 2 April 2020Thumbnail for version as of 21:02, 2 April 20201,776 × 1,600 (793 KB)Yomomo (talk | contribs)== {{int:filedesc}} == {{Information |Description={{en|1=This is a high-resolution version of Figure 1(b) from the paper "Hyperbolic entire functions with bounded Fatou components" by Bergweiler, Fagella and Rempe-Gillen (https://arxiv.org/abs/1404.0925). The Julia set is shown in black. The map is <math>f(z)=-z^2e^{1-z^2}</math>. Here there are superattracting fixed points at 0 and -1 (marked with filled circles), and 0 is an asymptotic value. The basin of 0 is coloured white and the basin o...

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