On questions of Fatou and Eremenko

Rippon, P.; Stallard, G.

doi:10.1090/S0002-9939-04-07805-0

On questions of Fatou and Eremenko
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by P. J. Rippon and G. M. Stallard

Proc. Amer. Math. Soc. 133 (2005), 1119-1126

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

Published electronically: October 18, 2004

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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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