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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The Schwarzian derivative and polynomial iteration
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by Hexi Ye
Conform. Geom. Dyn. 15 (2011), 113-132
Published electronically: August 16, 2011


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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Bibliographic 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:
  • MathSciNet review: 2833475