Meromorphic functions with linearly distributed values and Julia sets of rational functions
Complex Variables
2009-04-15 v1 Dynamical Systems
Abstract
If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if the Julia set of a rational function is contained in a smooth curve then it is contained in a circle.
Cite
@article{arxiv.0808.3800,
title = {Meromorphic functions with linearly distributed values and Julia sets of rational functions},
author = {Walter Bergweiler and Alexandre Eremenko},
journal= {arXiv preprint arXiv:0808.3800},
year = {2009}
}
Comments
6 pages