Open Access
2015 Constructing entire functions by quasiconformal folding
Christopher J. Bishop
Author Affiliations +
Acta Math. 214(1): 1-60 (2015). DOI: 10.1007/s11511-015-0122-0

Abstract

We give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of f. Among other applications, we construct a function f with bounded singular set, whose Fatou set contains a wandering domain.

Funding Statement

The author was partially supported by NSF Grant DMS 13-05233.

Citation

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Christopher J. Bishop. "Constructing entire functions by quasiconformal folding." Acta Math. 214 (1) 1 - 60, 2015. https://doi.org/10.1007/s11511-015-0122-0

Information

Received: 10 May 2013; Revised: 12 August 2014; Published: 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1338.30016
MathSciNet: MR3316755
Digital Object Identifier: 10.1007/s11511-015-0122-0

Keywords: area conjecture , bounded type , entire functions , Eremenko–Lyubich class , finite type , quasiconformal maps , Speiser class , tracts , transcendental dynamics , wandering domains

Rights: 2015 © Institut Mittag-Leffler

Vol.214 • No. 1 • 2015
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