The Schwarzian derivative and polynomial iteration

Details The Schwarzian derivative and polynomial iteration The Schwarzian derivative and polynomial iteration

2011-05-27

arxiv.org/abs/1105.5598v2

Mathematics

Dynamical Systems

Scientific paper

We consider the Schwarzian derivative $S_f$ of a complex polynomial $f$ and
its iterates. We show that the sequence $S_{f^n}/d^{2n}$ converges to
$-2(\partial G_f)^2$, for $G_f$ the escape-rate function of $f$. As a quadratic
differential, the Schwarzian derivative $S_{f^n}$ determines a conformal metric
on the plane. We study the ultralimit of these metric spaces.

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