Title
Rational Families Converging to a Family of Exponential Maps
Document Type
Article
Publication Date
2019
Department
Mathematics
Language
English
Publication Title
Journal of Fractal Geometry
Abstract
We analyze the dynamics of a sequence of families of non-polynomial rational maps, {f a,d }, for a ∈ C* = C \ {0}, d ≥ 2. For each d, {f a,d } is a family of rational maps of degree d of the Riemann sphere parametrized by a ∈ C*. For each a ∈ C* , as d → ∞, f a,d converges uniformly on compact sets to a map f a that is conformally conjugate to a transcendental entire map on C. We study how properties of the families f a,d 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.
Recommended Citation
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
Comments
For more information on the published version, visit The European Mathematical Society's Website.