Classification of 2-dimensional contracting rigid germs and Kato surfaces. I
type: Item
instance of: scholarly article
title: Classification of 2-dimensional contracting rigid germs and Kato surfaces. I
zbMATH Open document ID: 0983.32023
DOI: 10.1016/S0021-7824(00)00162-8
author: Charles Favre
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2000-10-29T00:00:00Z
review text: This paper is devoted to the analytic (and formal) classification of very special types of contracting germs in \((\mathbb{C}^2,0)\) and its application to the classification and the geometrical study of some compact analytic surfaces (Kato surfaces). The author classifies completely contracting rigid germs of \((\mathbb{C}^2,0)\) up to analytic and formal conjugacy and shows that these germs can be split into seven different classes. He shows that they are equivalent to very simple normal forms which are polynomial and their ``moduli'' spaces are finite-dimensional. Moreover, the authors gives an application to the study of the attraction of the superattracting point of a Hénon mapping [cf. \textit{J. H. Hubbard} and \textit{R. W. Oberste-Vorth}, Publ. Math. Inst. Hautes Étud. Sci. 79, 5-46 (1994; Zbl 0839.54029)].
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F99
Mathematics Subject Classification ID: 32B10
Mathematics Subject Classification ID: 32J05
Mathematics Subject Classification ID: 37C15
zbMATH DE Number: 1522072
zbMATH Keywords: classification of germs
zbMATH Keywords: formal conjugacy
zbMATH Keywords: moduli spaces
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1522072