Twist periodic solutions of second order singular differential equations
type: Item
instance of: scholarly article
title: Twist periodic solutions of second order singular differential equations
zbMATH Open document ID: 1172.34029
author: Jifeng Chu
author: Ming Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-06-10T00:00:00Z
review text: By definition, a periodic solution of a second order ODE is a twist solution if one of the nonlinear coefficients of the Birkhoff normal form of the Poincaré map is different from zero. A twist solution is in particular stable in the sense of Lyapunov. Generally speaking, the twist character of a periodic solution is determined by the third-order expansion of the Poincaré map, the so-called third-order approximation method. This paper continues the study initiated in previous works by the reviewer and provides new stability criteria for equations with repulsive singularities. The proofs involve careful estimates of the rotation number and the radial coordinate of the linerized equation.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 5563838
zbMATH Keywords: twist periodic solution
zbMATH Keywords: singular equations
zbMATH Keywords: third-order approximation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.02.033
OpenAlex ID: W2005488777
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DOI: 10.1016/J.JMAA.2009.02.033
description: scientific article; zbMATH DE number 5563838