Slow escaping points of meromorphic functions

Simple item page
dc.creatorRippon, P. J.
dc.creatorStallard, G. M.
dc.date2008-12-12
dc.date.accessioned2026-07-07T12:12:27Z
dc.date.available2026-07-07T12:12:27Z
dc.descriptionWe show that for any transcendental meromorphic function $f$ there is a point $z$ in the Julia set of $f$ such that the iterates $f^n(z)$ escape, that is, tend to $\infty$, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which $f^n(z)$ tends to $\infty$ at a bounded rate, and establish the connections between these sets and the Julia set of $f$. To do this, we show that the iterates of $f$ satisfy a strong distortion estimate in all types of escaping Fatou components except one, which we call a plane-filling wandering domain. We give examples to show how varied the structures of these slow escaping sets can be.
dc.identifierhttps://arxiv.org/abs/0812.2410
dc.identifierhttp://arxiv.org/abs/0812.2410
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210547
dc.subjectDynamical Systems
dc.subjectComplex Variables
dc.subject30D05; 37F10
dc.titleSlow escaping points of meromorphic functions
dc.typetext

Files

Collections

arXiv