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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 operator: sequences, fixed points and $N$-cycles
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by Stephen M. Zemyan
Conform. Geom. Dyn. 15 (2011), 44-49
Published electronically: April 25, 2011


Given a function $f(z)$ that is analytic in a domain $D$, we define the classical Schwarzian derivative $\{f,z\}$ of $f(z)$, and mention some of its most useful analytic properties. We explain how the process of iterating the Schwarzian operator produces a sequence of Schwarzian derivatives, and we illustrate this process with examples. Under a suitable restriction, these sequences become $N$-cycles of Schwarzian derivatives. Some properties of functions belonging to an $N$-cycle are listed. We conclude the article with a collection of related open problems.
  • Lars V. Ahlfors, Complex analysis, 3rd ed., International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable. MR 510197
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Bibliographic Information
  • Stephen M. Zemyan
  • Affiliation: Department of Mathematics, Penn State Mont Alto, Mont Alto, Pennsylvania 17237-9799
  • Email:
  • Received by editor(s): December 9, 2010
  • Published electronically: April 25, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 15 (2011), 44-49
  • MSC (2010): Primary 34L30; Secondary 30D30, 34A25, 34A34
  • DOI:
  • MathSciNet review: 2801171