Stability criterion for the resonance 1:3
type: Item
instance of: scholarly article
title: Stability criterion for the resonance 1:3
zbMATH Open document ID: 0711.34067
author: A. B. Kosterin
published in: Moscow University Mathematics Bulletin
publication date: 1990-01-01T00:00:00Z
review text: The paper is devoted to the investigation of fourth order systems \(\dot u=f(u)\), \(f(0)=0\), \(u\in {\mathbb{R}}^ 4\), where the matrix \((\partial f/\partial u)|_{u=0}\) has the two pairs of purely imaginary eigenvalues \(\pm i\omega\), \(\pm 3i\omega\). By passing to an appropriate factor system the author obtains a stability criterion which is slightly more general than a criterion given by \textit{L. G. Khazin} and \textit{Eh. Eh. Shnol'} [Prikl. Mat. Mekh. 44, 229-237 (1980; Zbl 0465.34033)]. Nevertheless, as the author regrets, the question of an exact analytic solution of the stability problem in this case remains open.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 4169136
zbMATH Keywords: fourth order systems
zbMATH Keywords: stability criterion
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4169136