The Schwarzian derivative and polynomial iteration
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2011
- DOI:
- 10.48550/arXiv.1105.5598
- arXiv:
- arXiv:1105.5598
- Bibcode:
- 2011arXiv1105.5598Y
- Keywords:
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- Mathematics - Dynamical Systems