Escaping points of entire functions of small growth

dc.creatorRippon, P. J.
dc.creatorStallard, G. M.
dc.date2008-01-23
dc.date.accessioned2026-07-07T08:56:05Z
dc.date.available2026-07-07T08:56:05Z
dc.descriptionLet $f$ 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.identifierhttps://arxiv.org/abs/0801.3605
dc.identifierhttp://arxiv.org/abs/0801.3605
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146486
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject30D05; 37F10
dc.titleEscaping points of entire functions of small growth
dc.typetext

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