On continuous dynamics of automorphisms of \(\mathbb{C}^ 2\)
type: Item
instance of: scholarly article
title: On continuous dynamics of automorphisms of \(\mathbb{C}^ 2\)
zbMATH Open document ID: 0812.32012
DOI: 10.1007/BF02567061
author: Chiara de Fabritiis
published in: Manuscripta Mathematica
publication date: 1994-01-26T00:00:00Z
full work available at URL: https://eudml.org/doc/155786
review text: The author studies one-parameter subgroups of the group of polynomial automorphisms of \(\mathbb{C}^ 2\) and of the shear group of \(\mathbb{C}^ 2\) defined by \textit{J.-P. Rosay} and \textit{W. Rudin} [Trans. Am. Math. Soc. 310, No. 1, 47-86 (1988; Zbl 0708.58003)]. It is shown that such a subgroup is conjugate to a one-parameter group in the group of all affine transformations of \(\mathbb{C}^ 2\) or in the group of elementary automorphisms of the group of polynomial automorphisms of \(\mathbb{C}^ 2\). As an application one obtains some results about the asymptotic behaviour of one-parameter subgroups in each of these two settings.
reviewed by: Bruce Gilligan
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 490674
zbMATH Keywords: one-parameter subgroups
zbMATH Keywords: polynomial automorphisms
zbMATH Keywords: affine transformations
MaRDI profile type: Publication
cites work: Volume-preserving automorphisms of C⊃n⊃
cites work: Polynomial flows in the plane
cites work: Q3981482
cites work: Polynomial Diffeomorphisms of C 2 . II: Stable Manifolds and Recurrence
cites work: Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). III: Ergodicity, exponents and entropy of the equilibrium measure
cites work: Dynamical properties of plane polynomial automorphisms
cites work: Über ganze birationale Transformationen der Ebene.
cites work: Q5818521
cites work: Holomorphic Maps from C n to C n
description: scientific article; zbMATH DE number 490674