Meromorphic functions with two completely invariant domains
Complex Variables
2009-09-29 v2 Dynamical Systems
Abstract
We show that if a meromorphic function has two completely invariant Fatou components and only finitely many critical and asymptotic values, then its Julia set is a Jordan curve. However, even if both domains are attracting basins, the Julia set need not be a quasicircle. We also show that all critical and asymptotic values are contained in the two completely invariant components. This need not be the case for functions with infinitely many critical and asymptotic values.
Keywords
Cite
@article{arxiv.math/0310495,
title = {Meromorphic functions with two completely invariant domains},
author = {Walter Bergweiler and Alexandre Eremenko},
journal= {arXiv preprint arXiv:math/0310495},
year = {2009}
}
Comments
14 pages, 6 figures, Examples 3 and 4 have been replaced by a simpler example, minor corrections made