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Conformal Geometry and Dynamics

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The Schwarzian derivative and polynomial iteration

Author: Hexi Ye
Journal: Conform. Geom. Dyn. 15 (2011), 113-132
MSC (2010): Primary 37F10; Secondary 37F40
Published electronically: August 16, 2011
MathSciNet review: 2833475
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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.

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Additional Information

Hexi Ye
Affiliation: University of Illinois at Chicago, Department of Mathematics and Computer Science, MC 249, 851 S. Morgan Street, Chicago, Illinois 60607-7045

Received by editor(s): June 17, 2011
Published electronically: August 16, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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