The schwarzian operator

Sequences, fixed points and N-cycles

Stephen Michael Zemyan

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)44-49
Number of pages6
JournalConformal Geometry and Dynamics
Volume15
Issue number4
DOIs
StatePublished - Apr 25 2011

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Schwarzian Derivative
Fixed point
Cycle
Operator
Open Problems
Restriction

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Zemyan, Stephen Michael. / The schwarzian operator : Sequences, fixed points and N-cycles. In: Conformal Geometry and Dynamics. 2011 ; Vol. 15, No. 4. pp. 44-49.
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The schwarzian operator : Sequences, fixed points and N-cycles. / Zemyan, Stephen Michael.

In: Conformal Geometry and Dynamics, Vol. 15, No. 4, 25.04.2011, p. 44-49.

Research output: Contribution to journalArticle

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