Rational functions with real multipliers
Dynamical Systems
2012-02-07 v1 Complex Variables
Abstract
Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle.
Keywords
Cite
@article{arxiv.0810.2260,
title = {Rational functions with real multipliers},
author = {Alexandre Eremenko and Sebastian van Strien},
journal= {arXiv preprint arXiv:0810.2260},
year = {2012}
}
Comments
16 pages 1 figure