## The Schwarzian derivative and polynomial iteration

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- by Hexi Ye PDF
- Conform. Geom. Dyn.
**15**(2011), 113-132 Request permission

## 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.## References

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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
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**15**(2011), 113-132 - MSC (2010): Primary 37F10; Secondary 37F40
- DOI: https://doi.org/10.1090/S1088-4173-2011-00229-3
- MathSciNet review: 2833475