Fast escaping points of entire functions: A new regularity condition

Evdoridou, V. (2016). Fast escaping points of entire functions: A new regularity condition. Mathematical Proceedings of the Cambridge Philosophical Society, 160(1) pp. 95–106.

DOI: https://doi.org/10.1017/S0305004115000602

Abstract

Let ƒ be a transcendental entire function. The fast escaping set, A(ƒ), plays a key role in transcendental dynamics. The quite fast escaping set, Q(ƒ), defined by an apparently weaker condition is equal to A(ƒ) under certain conditions. Here we introduce Q₂(ƒ) defined by what appears to be an even weaker condition. Using a new regularity condition we show that functions of finite order and positive lower order satisfy Q₂(ƒ) = A(ƒ). We also show that the finite composition of such functions satisfies Q₂(ƒ) = A(ƒ). Finally, we construct a function for which Q₂(ƒ) ≠ Q(ƒ) = A(ƒ).

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