# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332009

Acta Mathematica, 203, (2), 235-267, 2008.3
We prove an analog of Böttcher’s theorem for transcendental entire functions in the Eremenko–Lyubich class $\mathcal{B}$ . More precisely, let$f$and$g$be entire functions with bounded sets of singular values and suppose that$f$and$g$belong to the same parameter space (i.e., are$quasiconformally equivalent$in the sense of Eremenko and Lyubich). Then$f$and$g$are conjugate when restricted to the set of points that remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane.
@inproceedings{lasse2008rigidity,
title={Rigidity of escaping dynamics for transcendental entire functions},
author={Lasse Rempe},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203354378790718},
booktitle={Acta Mathematica},
volume={203},
number={2},
pages={235-267},
year={2008},
}

Lasse Rempe. Rigidity of escaping dynamics for transcendental entire functions. 2008. Vol. 203. In Acta Mathematica. pp.235-267. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203354378790718.