On the instability of Herman rings
type: Item
instance of: scholarly article
title: On the instability of Herman rings
zbMATH Open document ID: 0595.30032
DOI: 10.1007/BF01388582
author: Ricardo Mañé
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143268
review text: Denote by E the space of rational self-maps, of degree greater than one, of the Riemann sphere, furnished with the \(C^ 0\) topology. A Herman ring R of \(f\in E\) is a component of the complement of the Julia set of f, which is homeomorphic to an annulus and mapped to itself by some iterate \(f^ n\) of f, which is analytically conjugate to a rotation in R. The author shows that those f, which do not possess Herman rings, form an open dense subset of E. This extends the approach of the author, \textit{P. Sad} and \textit{D. Sullivan}, Ann. Sci. Éc. Norm. Supér., IV. Sér. 16, 193-217 (1983; Zbl 0524.58025), to the discussion of whether hyperbolic members are dense in E.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 3957553
zbMATH Keywords: rational map
zbMATH Keywords: Herman ring
MaRDI profile type: Publication
cites work: Q5512337
cites work: On the dynamics of rational maps
OpenAlex ID: W1501435655
description: scientific article; zbMATH DE number 3957553