Acta Mathematica

Constructing entire functions by quasiconformal folding

Christopher J. Bishop

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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.


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

Article information

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

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

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

2015 © Institut Mittag-Leffler


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

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