Unicritical Blaschke Products and Domains of Ellipticity

• Alastair Fletcher ^[1]
  1. [1] Northern Illinois University

     Northern Illinois University

     Township of DeKalb, Estados Unidos

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 1, 2015, págs. 25-38
• Idioma: inglés
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• Resumen

  • Elliptic Möbius transformations of the unit disk are those for which there is a fixed point in D. It is not hard to classify which Möbius transformations are elliptic in terms of the parameters. The set of parameters can be identified with the solid torus S1 × D, and the set of elliptic parameters is called the domain of ellipticity. In this paper, we study the domain of ellipticity for non-trivial unicritical Blaschke products.

    We will also study the set corresponding to the Mandelbrot set for this family, and show how it can be obtained from the domain of ellipticity by adding one point.