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.

Comments

For more information on the published version, visit The European Mathematical Society's Website.

Full text currently unavailable.

COinS