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arXiv · 1510.07449

Fatou's web

Vasiliki Evdoridou
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Abstract

Let $f$ be Fatou's function, that is, $f(z)= z+1+e^{-z}$. We prove that the escaping set of $f$ has the structure of a `spider's web' and we show that this result implies that the non-escaping endpoints of the Julia set of $f$ together with infinity form a totally disconnected set. We also give a well-known transcendental entire function, due to Bergweiler, for which the escaping set is a spider's web and we point out that the same property holds for families of functions.

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Vasiliki Evdoridou. 2015-10-26. Fatou's web. https://arxiv.org/abs/1510.07449

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