The Schwarzian derivative and polynomial iteration
Dynamical Systems
2011-06-07 v2
Abstract
We consider the Schwarzian derivative of a complex polynomial and its iterates. We show that the sequence converges to , for the escape-rate function of . As a quadratic differential, the Schwarzian derivative determines a conformal metric on the plane. We study the ultralimit of these metric spaces.
Cite
@article{arxiv.1105.5598,
title = {The Schwarzian derivative and polynomial iteration},
author = {Hexi Ye},
journal= {arXiv preprint arXiv:1105.5598},
year = {2011}
}