Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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
HTML articles powered by AMS MathViewer

by Stephen M. Zemyan PDF
Conform. Geom. Dyn. 15 (2011), 44-49 Request permission

Abstract:

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.
References
  • 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
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 34L30, 30D30, 34A25, 34A34
  • Retrieve articles in all journals with MSC (2010): 34L30, 30D30, 34A25, 34A34
Additional Information
  • Stephen M. Zemyan
  • Affiliation: Department of Mathematics, Penn State Mont Alto, Mont Alto, Pennsylvania 17237-9799
  • Email: smz3@psu.edu
  • 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: https://doi.org/10.1090/S1088-4173-2011-00224-4
  • MathSciNet review: 2801171