Rational families converging to a family of exponential maps
type: Item
instance of: scholarly article
title: Rational families converging to a family of exponential maps
zbMATH Open document ID: 1475.37050
DOI: 10.4171/JFG/70
author: Joanna Furno
author: Lorelei Koss
author: Jane Hawkins
published in: Journal of Fractal Geometry
publication date: 2019-03-14T00:00:00Z
review text: Summary: We analyze the dynamics of a sequence of families of non-polynomial rational maps, \(\{f_{a,d}\}\), for \(a \in \mathbb C^*= \mathbb C \setminus \{0\}, d \geq 2\). For each \(d\), \(\{f_{a,d}\}\) is a family of rational maps of degree \(d\) of the Riemann sphere parametrized by \(a \in \mathbb C^*\). For each \(a \in \mathbb C^*\), as \(d \rightarrow \infty\), \(f_{a,d}\) converges uniformly on compact sets to a map \(f_a\) that is conformally conjugate to a transcendental entire map on \(\mathbb C\). 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.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F46
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 7036249
zbMATH Keywords: complex dynamics
zbMATH Keywords: Julia sets
zbMATH Keywords: rational maps
zbMATH Keywords: entire functions
MaRDI profile type: Publication
Wikidata QID: Q115481585
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full work available at URL: https://doi.org/10.4171/jfg/70
OpenAlex ID: W2912648804
description: scientific article; zbMATH DE number 7036249