Relating Singularly Perturbed Rational Maps to Families of Entire Maps
Contemporary Mathematics: Dynamical Systems and Random Processes
In the publication,
Furno, Joanna, Jane Hawkins, and Lorelei Koss. "Rational Families Converging to a Family of Exponential Maps." Journal of Fractal Geometry 6, no. 1 (2019): 89-108. https://www.ems-ph.org/journals/show_abstract.php?issn=2308-1309&vol=6&iss=1&rank=4,
Hawkins and the authors of this paper analyzed the dynamics of a sequence of families of rational maps fa,d(z) = az(1 + 1/(zd))d and the limiting family as d→∞, fa(z) = aze1/z. In this paper, we study the dynamics of related sequences of families of rational maps and their limiting families.
Furno, Joanna, and Lorelei Koss. "Relating Singularly Perturbed Rational Maps to Families of Entire Maps." In Dynamical Systems and Random Processes, edited by Jane Hawkins, Rachel L. Rossetti, and Jim Wiseman, Contemporary Mathematics 736 (2019): 49-68.