English

The Schwarzian derivative and polynomial iteration

Dynamical Systems 2011-06-07 v2

Abstract

We consider the Schwarzian derivative SfS_f of a complex polynomial ff and its iterates. We show that the sequence Sfn/d2nS_{f^n}/d^{2n} converges to 2(Gf)2-2(\partial G_f)^2, for GfG_f the escape-rate function of ff. As a quadratic differential, the Schwarzian derivative SfnS_{f^n} 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}
}
R2 v1 2026-06-21T18:13:45.272Z