Escaping points of entire functions of small growth

Rippon, P. J. and Stallard, G. M. (2009). Escaping points of entire functions of small growth. Mathematische Zeitschrift, 261(3) pp. 557–570.

DOI: https://doi.org/10.1007/s00209-008-0339-0

Abstract

Let f be a transcendental entire function and let I(f) denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions, I(f) is connected. In particular, we show that I(f) is connected if f has order zero and sufficiently small growth or has order less than 1/2 and regular growth. This shows that, for these functions, Eremenko’s conjecture that I(f) has no bounded components is true. We also give a new criterion related to I(f) which is sufficient to ensure that f has no unbounded Fatou components.

Viewing alternatives

Look up in Google Scholar

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions
No digital document available to download for this item

Item Actions

Export

About

CORE (COnnecting REpositories)

Recommendations