Regularity and growth conditions for fast escaping points of entire functions

Abstract

Abstract. Let f be a transcendental entire function. The fast escaping set A(f ) plays a key role in transcendental dynamics and so it is useful to be able to identify points in this set. Recently it was shown that, under certain conditions, the quite fast escaping set, Q(f ), and the related set Q 2 (f ), are equal to A(f ). In this paper we generalise these sets by introducing a family of sets Q m (f ), m ∈ N, and give several conditions under which Q m (f ) is equal to A(f ).