Linearization of Hénon maps with resonant eigenvalues at an attracting fixed point
type: Item
instance of: scholarly article
title: Linearization of Hénon maps with resonant eigenvalues at an attracting fixed point
zbMATH Open document ID: 1417.32020
author: David Hahn
published in: Complex Analysis and Operator Theory
publication date: 2018-02-13T00:00:00Z
review text: The paper under review deals with the problem of local holomorphic linearization of attracting Hénon maps in $\mathbb{C}^2$ at a fixed point. It is well known that if there are no resonances between the eigenvalues of the linear part then holomorphic linearization is always possible. The author addresses the question of whether the presence of resonances does always prevent holomorphic linearization. He provides explicit examples of Hénon maps of arbitrary degree $d\ge 3$ which, despite having resonances, are holomorphically linearizable. In the case of Hénon maps of degree $d=2$, he proves that resonances of order $k=2, 3, 4, 5, 6$ always prevent holomorphic linearization and presents examples of maps with resonances of degree $k=7, 8, 9, 10, 11, 12$ which are linearizable.
reviewed by: L. López-Hernanz
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 6837886
zbMATH Keywords: local holomorphic dynamics
zbMATH Keywords: Hénon maps
zbMATH Keywords: resonances
zbMATH Keywords: attracting fixed point
MaRDI profile type: Publication
full work available at URL: s11785-017-0722-0
OpenAlex ID: W2752610461
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DOI: 10.1007/S11785-017-0722-0
description: scientific article; zbMATH DE number 6837886