Periodic solutions of a Newtonian equation: Stability by the third approximation
type: Item
instance of: scholarly article
title: Periodic solutions of a Newtonian equation: Stability by the third approximation
zbMATH Open document ID: 0855.34058
author: Rafael Ortega
published in: Journal of Differential Equations
publication date: 1997-02-16T00:00:00Z
review text: A scalar differential Newtonian equation of the form (1) \(x'' = f(t,x)\) where \(f\) is periodic in time \(t\) is considered. It is known that in the neighbourhood of an elliptic periodic solution \(\Theta\) of (1) a so-called Birkhoff normal form with twist coefficients can be found. The twist coefficients depend on derivatives of \(f\) (evaluated at \(\Theta)\) up to the order \((2n - 1)\). Sufficient conditions of stability of the periodic solutions \(\Theta\) are found in the article on the basis of analysis of the values of the twist coefficients.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 910000
zbMATH Keywords: differential Newtonian equation
zbMATH Keywords: Birkhoff normal form
zbMATH Keywords: twist coefficients
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0103
OpenAlex ID: W2089059683
DOI: 10.1006/JDEQ.1996.0103
description: scientific article; zbMATH DE number 910000