Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\)
type: Item
instance of: scholarly article
title: Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\)
zbMATH Open document ID: 0832.58031
DOI: 10.5565/PUBLMAT_38294_16
author: Monique Hakim
published in: Publicacions Matemàtiques
publication date: 1996-03-07T00:00:00Z
full work available at URL: https://eudml.org/doc/41174
review text: A germ \(F\) of analytic transformation of \((\mathbb{C}^p, 0)\) is called semi-attractive at the origin, if \(F_{(0)}'\) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or \(F-I\) has multiplicity \(k\) and there exists a domain of attraction with \(k - 1\) petals. The case where \(F\) is a global isomorphism of \(C^2\) and \(F - I\) has multiplicity \(k\) at the origin is also studied.
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 791196
zbMATH Keywords: semi-attractive transformations
zbMATH Keywords: domain of attraction
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 791196