Dynamics of normalized systems on surfaces
type: Item
instance of: scholarly article
title: Dynamics of normalized systems on surfaces
zbMATH Open document ID: 1076.34036
DOI: 10.12775/TMNA.2004.022
published in: Topological Methods in Nonlinear Analysis
publication date: 2005-03-30T00:00:00Z
review text: This paper is an extension of previous results obtained by the author on the dynamics of commuting systems on two-dimensional manifolds [Ann. Mat. Pura Appl., IV. Ser. 173, 213--232 (1997; Zbl 0941.34018)]. More precisely, it is on a pair of two-dimensional autonomous ordinary differential equations satisfying some conditions for commuting. Among the earlier results can be noted: centers are isochronous, critical (or stationary) points have positive index, limit cycles do not exist, attraction and central regions are unbounded. The notions of normalizer and commutators are introduced. It is claimed that passing from commutators to normalizers one has the advantage to consider a wider class of systems. In this framework, several dynamical properties of couples of commuting systems are extended to normalized systems. A coarse classification of the dynamics generated by normalized vector fields on two-dimensional compact connected oriented manifolds is presented.
reviewed by: Christian Mira
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 2149530
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: vector fields
zbMATH Keywords: normalizer
zbMATH Keywords: Euler characteristic
author: Marco Sabatini
MaRDI profile type: Publication
full work available at URL: tmna.2004.022
OpenAlex ID: W1606042550
description: scientific article; zbMATH DE number 2149530