Escaping points of entire functions of small growth
| dc.creator | Rippon, P. J. | |
| dc.creator | Stallard, G. M. | |
| dc.date | 2008-01-23 | |
| dc.date.accessioned | 2026-07-07T08:56:05Z | |
| dc.date.available | 2026-07-07T08:56:05Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0801.3605 | |
| dc.identifier | http://arxiv.org/abs/0801.3605 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146486 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | 30D05; 37F10 | |
| dc.title | Escaping points of entire functions of small growth | |
| dc.type | text |