Attracting basins for automorphisms of \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Attracting basins for automorphisms of \(\mathbb{C}^2\)
zbMATH Open document ID: 0932.37028
author: Brendan J. Weickert
published in: Inventiones Mathematicae
publication date: 2000-03-19T00:00:00Z
review text: The paper deals with the interesting question whether an automorphism of \(\mathbb{C}^n\) tangent to the identity can have a domain of attraction, and if so, whether that domain is biholomorphic to \(\mathbb{C}^n\). It is obvious that this cannot happen when \(n=1\), due to the fact that the automorphism group of \(\mathbb{C}\) is the group of affine mappings \(z\mapsto az+b\), \(a\neq 0\). The main result of the paper states that there exist an automorphism \(\mathbb{C}^2\) tangent to the identity with an invariant domain of attraction to the origin, biholomorphic to \(\mathbb{C}^2\), on which the automorphism is biholomorphic conjugate to the map \((x,y)\mapsto(x-1,y)\).
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F15
zbMATH DE Number: 1186152
zbMATH Keywords: automorphisms of \(\mathbb{C}^n\)
zbMATH Keywords: domain of attraction
zbMATH Keywords: biholomorphic
zbMATH Keywords: conjugacy
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s002220050234
OpenAlex ID: W2027095416
DOI: 10.1007/S002220050234
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description: scientific article; zbMATH DE number 1186152