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Exotic Baker and wandering domains for Ahlfors island maps

Rempe, Lasse and Rippon, Philip (2012). Exotic Baker and wandering domains for Ahlfors island maps. Journal d'Analyse Mathematique, 117(1) pp. 297–319.

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Let X be a Riemann surface of genus at most 1, i.e. X is the Riemann sphere or a torus. We construct a variety of examples of analytic functions g : W → X, where W is an arbitrary subdomain of X, that satisfy Epstein’s “Ahlfors islands condition”. In particular, we show that the accumulation set of any curve tending to the boundary of W can be realized as the omega-limit set of a Baker domain of such a function. As a corollary of our construction, we show that there are entire functions with Baker domains in which the iterates converge to infinity arbitrarily slowly. We also construct Ahlfors islands maps with wandering domains and logarithmic singularities, as well as examples where X is a compact hyperbolic surface.

Item Type: Journal Article
Copyright Holders: 2012 Springer
ISSN: 1565-8538
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
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Item ID: 31618
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 11:51
Last Modified: 18 Jan 2016 12:01
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