Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 875-888

REGULARITY AND GROWTH CONDITIONS FOR FAST ESCAPING POINTS OF ENTIRE FUNCTIONS

Vasiliki Evdoridou

The Open University, Department of Mathematics and Statistics
Walton Hall, Milton Keynes MK7 6AA, U.K.; vasiliki.evdoridou 'at' open.ac.uk

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 Q₂(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).

2010 Mathematics Subject Classification: Primary 37F10; Secondary 30D05.

Key words: Entire function, fast escaping set, quite fast escaping set, regularity, finite order, positive lower order.

Reference to this article: V. Evdoridou: Regularity and growth conditions for fast escaping points of entire functions. Ann. Acad. Sci. Fenn. Math. 42 (2017), 875-888.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4258