The Schwarzian derivative and polynomial iteration
Abstract
We consider the Schwarzian derivative Sf of a complex polynomial f and its iterates. We show that the sequence Sfn/d2n converges to -2(∂ Gf)2, for Gf the escape-rate function of f. As a quadratic differential, the Schwarzian derivative Sfn determines a conformal metric on the plane. We study the ultralimit of these metric spaces.
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