# Boundaries of escaping Fatou components

Rippon, P. J. and Stallard, G. M. (2011). Boundaries of escaping Fatou components. Proceedings of the American Mathematical Society, 139(8) pp. 2807–2820.

## Abstract

Let be a transcendental entire function and be a Fatou component of . We show that if is an escaping wandering domain of , then most boundary points of (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of are escaping, then is an escaping Fatou component. Some applications of these results are given; for example, if is the escaping set of , then is connected.

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