The schwarzian operator: Sequences, fixed points and N-cycles

Stephen M. Zemyan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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
Issue number4
StatePublished - Apr 25 2011

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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