On questions of Fatou and Eremenko

Rippon, P.J. and Stallard, G.M. (2005). On questions of Fatou and Eremenko. Proceedings of the American Mathematical Society, 133(4) pp. 1119–1126.

DOI: https://doi.org/10.1090/S0002-9939-04-07805-0

Abstract

Let $f$ be a transcendental entire function and let $I(f)$ be the set of points whose iterates under $f$ tend to infinity. We show that $I(f)$ has at least one unbounded component. In the case that $f$ has a Baker wandering domain, we show that $I(f)$ is a connected unbounded set.

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