Quasiregular analogues of critically finite rational functions with parabolic orbifold
type: Item
instance of: scholarly article
title: Quasiregular analogues of critically finite rational functions with parabolic orbifold
zbMATH Open document ID: 0911.30018
DOI: 10.1007/BF02788694
author: Volker Mayer
published in: Journal d'Analyse Mathématique
publication date: 1999-05-16T00:00:00Z
review text: Let \(\Gamma\) be a discrete group of isometries of \(\mathbb{R}^n\) and let \(h:\mathbb{R}^n\to \overline{\mathbb{R}}^n\) a quasiregular automorphic mapping with respect to \(\Gamma\) [\textit{O. Martio} and \textit{U. Srebro}, J. Anal. Math. 28, 20-40 (1975; Zbl 0317.30025)]. There exists a uniformly quasiregular mapping \(f\) of \(\overline{\mathbb{R}}^n\) satisfying Schröder's equation \(f\circ h=h\circ A\) where a given similarity \(A\) is such that \(A\circ \Gamma\circ A^{-1}\subset \Gamma\); \(f\) is called a mapping of Lattès-type. The non-injective Lattès-type mapping \(f\) is characterized by the property that it has an \(f\)-invariant conformal structure which is flat at the repelling fixed point of some iterate \(f^k\) of \(f\). The paper also contains interesting examples of Lattés-type mappings.
reviewed by: O. Martio
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 1221951
zbMATH Keywords: quasiregular
zbMATH Keywords: automorphic mappings
zbMATH Keywords: Lattès-type mapping
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02788694
OpenAlex ID: W2029084026
description: scientific article; zbMATH DE number 1221951