The characterization of degenerate and non-degenerate systems
type: Item
instance of: scholarly article
title: The characterization of degenerate and non-degenerate systems
zbMATH Open document ID: 0591.34038
DOI: 10.1216/RMJ-1986-16-1-203
author: Raúl Manásevich
author: Alan R. Hausrath
published in: Rocky Mountain Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(x=0\) be a center of the differential equation (1) \(x'=F(x)\). We say that a T-periodic solution u of (1) is non-degenerate if and only if every T-periodic solution of the linear variational equation (2) \(y'=F_ x(u(t))y\) is a multiple of u'(t). The authors use elementary methods to obtain sufficient conditions for every periodic solution of (1) in some neighborhood of the origin to be non-degenerate. The question of non- degeneracy is important in the study of periodic solutions of the weakly perturbed equation (3) \(x'=F(x)+ef(t,x)\) where e is a small parameter.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 3948791
zbMATH Keywords: first order differential equation
zbMATH Keywords: linear variational equation
zbMATH Keywords: weakly perturbed equation
zbMATH Keywords: small parameter
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3948791