Components of degree two hyperbolic rational maps
type: Item
instance of: scholarly article
title: Components of degree two hyperbolic rational maps
zbMATH Open document ID: 0712.30022
DOI: 10.1007/BF01231191
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143789
review text: The author considers rational maps f of degree 2 which are hyperbolic in the sense that the orbits of the critical points are bounded away from the Julia set of f. These maps are classified into four distinct types. The paper describes the components of the set of these hyperbolic maps. Each component consists of maps of the same type. A rather long theorem describes the structure of the components of different types. There is a discussion of the boundary points of some of the components. Rather than using quasiconformal techniques the author relies on a result (described in a preprint of W. P. Thurston) on the equivalence of certain branched coverings of the sphere to a rational map.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 4171294
zbMATH Keywords: hyperbolic rational map
zbMATH Keywords: Julia set
author: Mary Rees
MaRDI profile type: Publication
cites work: Invariant sets under iteration of rational functions
cites work: Q3941647
cites work: On the dynamics of rational maps
cites work: Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
description: scientific article; zbMATH DE number 4171294