Kupka-Smale theorem for automorphisms of \(\mathbf C^n\)
type: Item
instance of: scholarly article
title: Kupka-Smale theorem for automorphisms of \(\mathbf C^n\)
zbMATH Open document ID: 0946.32012
DOI: 10.1215/S0012-7094-98-09317-6
author: Greg Buzzard
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: It is well known that the Kupka-Smale theorem is an important and useful tool in the study of dynamical systems. Briefly, this theorem says that for a generic diffeomorphism, all periodic points are transverse. The goal of the paper under review is to prove this theorem for the space Aut\((\mathbb{C}^n) \) of biholomorphic automorphisms of \( \mathbb{C}^n, \;n \geq 2\).
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32M17
zbMATH DE Number: 1425127
zbMATH Keywords: Kupka-Smale theorem
zbMATH Keywords: automorphisms of \( \mathbb{C} ^n \)
reviewed by: Mircea Puta
MaRDI profile type: Publication
cites work: From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems
cites work: Infinitely many periodic attractors for holomorphic maps of 2 variables
cites work: An interpolation theorem for holomorphic automorphisms of \({\mathbb{C}}^n\)
cites work: Q3993490
cites work: Interpolation by holomorphic automorphisms and embeddings in \({\mathbb{C}}^n\)
cites work: Q4134602
cites work: Q5529175
cites work: Q3346966
cites work: Introduction to the theory of analytic spaces
cites work: Holomorphic Maps from C n to C n
cites work: Q4340161
cites work: Endomorphisms of Compact Differentiable Manifolds
cites work: Q3744918
cites work: Q5720367
cites work: Stable manifolds of automorphisms of at fixed points
description: scientific article; zbMATH DE number 1425127