Fatou’s web

Evdoridou, V.

doi:10.1090/proc/13150

Fatou’s web
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by V. Evdoridou PDF

Proc. Amer. Math. Soc. 144 (2016), 5227-5240 Request permission

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 present 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 some families of functions.

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