On the degree of iterates of automorphisms of the affine plane
type: Item
instance of: scholarly article
title: On the degree of iterates of automorphisms of the affine plane
zbMATH Open document ID: 0944.32017
published in: Manuscripta Mathematica
publication date: 2000-09-11T00:00:00Z
review text: Let \(f\) be a polynomial automorphism of the affine space \(\mathbb C^2\). The author studies the iterations \(f^n=f\circ\cdots\circ f\) of \(f\). Let \(\tau:=\deg f^2\slash\deg f\). He proves that: 1. If \(\tau\leq 1\) then the sequence \((\deg f^n)_{n\in\mathbb N}\) is periodic for large \(n\), 2. If \(\tau>1\) then \(\tau\) is an integer and the sequence \((\deg f^n)_{n\in\mathbb N}\) is a geometric progression of the ratio \(\tau\).
Mathematics Subject Classification ID: 32H50
zbMATH DE Number: 1275772
zbMATH Keywords: polynomial automorphism
zbMATH Keywords: amalgamated product
zbMATH Keywords: iterate of an automorphism
author: Jean-Philippe Furter
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
full work available at URL: s002290050134
OpenAlex ID: W2061032121
DOI: 10.1007/S002290050134
description: scientific article; zbMATH DE number 1275772