Acta Mathematica

Constructing entire functions by quasiconformal folding

Christopher J. Bishop

Full-text: Open access

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.

Note

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

Article information

Source
Acta Math., Volume 214, Number 1 (2015), 1-60.

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485802411

Digital Object Identifier
doi:10.1007/s11511-015-0122-0

Mathematical Reviews number (MathSciNet)
MR3316755

Zentralblatt MATH identifier
1338.30016

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

Rights
2015 © Institut Mittag-Leffler

Citation

Bishop, Christopher J. Constructing entire functions by quasiconformal folding. Acta Math. 214 (2015), no. 1, 1--60. doi:10.1007/s11511-015-0122-0. https://projecteuclid.org/euclid.acta/1485802411


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