On the dynamics of \(n\)-dimensional quadratic endomorphisms
type: Item
instance of: scholarly article
title: On the dynamics of \(n\)-dimensional quadratic endomorphisms
zbMATH Open document ID: 0929.37014
published in: Communications in Mathematical Physics
publication date: 1999-06-02T00:00:00Z
review text: Let \(F= (f_1,\dots, f_n)\) be a \(C^2\)-convex endomorphism; for \(\nu\in \mathbb{R}^n\) fixed, consider the one parameter family \(F_\mu= F- \mu\nu\). The authors find sufficient conditions on the geometry of intersections of the level sets of the functions \(f_i\) such that for large values of \(\mu\), the map \(F_\mu\) belongs to some class \({\mathcal H}_0\), for which the dynamical behaviour is completely described, namely: either the nonwandering set \(\Omega(F_\mu)\) is empty or \(F_\mu\) restricted to \(\Omega(F_\mu)\) is an expanding map. The authors show that these conditions (sufficient) are generic in the space of quadratic endomorphisms.
Mathematics Subject Classification ID: 37F15
Mathematics Subject Classification ID: 37G30
zbMATH DE Number: 1294603
zbMATH Keywords: convex endomorphism
zbMATH Keywords: nonwandering set
zbMATH Keywords: expanding map
zbMATH Keywords: quadratic endomorphisms
author: N. Romero
author: A. Rovella
author: F. Vilamajó
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s002200050390
OpenAlex ID: W2089223094
DOI: 10.1007/S002200050390
description: scientific article; zbMATH DE number 1294603