Rational families converging to a family of exponential maps

  • Joanna Furno

    University of Houston, USA
  • Jane Hawkins

    University of North Carolina at Chapel Hill, USA
  • Lorelei Koss

    Dickinson College, Carlisle, USA
Rational families converging to a family of exponential maps cover

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Abstract

We analyze the dynamics of a sequence of families of non-polynomial rational maps, , for . For each , is a family of rational maps of degree of the Riemann sphere parametrized by . For each , as , converges uniformly on compact sets to a map that is conformally conjugate to a transcendental entire map on . We study how properties of the families contribute to our understanding of the dynamical properties of the limiting family of maps. We show all families have a common connectivity locus; moreover the rational maps contain some well-studied examples.

Cite this article

Joanna Furno, Jane Hawkins, Lorelei Koss, Rational families converging to a family of exponential maps. J. Fractal Geom. 6 (2019), no. 1, pp. 89–108

DOI 10.4171/JFG/70