Two problems about pseudolinear systems
type: Item
instance of: scholarly article
title: Two problems about pseudolinear systems
zbMATH Open document ID: 0811.34019
published in: Chinese Science Bulletin
publication date: 1995-05-07T00:00:00Z
review text: The subject of this note are generalized Liénard systems \(\dot x = a(x) + b(y)\), \(\dot y = c(x) + d(y)\), where the right hand side is differentiable in \(\mathbb{R}^ 2\) and the origin is the only equilibrium. In answering a question asked by R. Conti, the author presents examples of such systems for which a) the origin is a center-focus, i.e., in any neighborhood of the origin, there are both closed and nonclosed orbits; b) the origin belongs to the \(\omega\)-limit set of each point \((x,y) \in \mathbb{R}^ 2\), but is not globally attractive; c) the origin is globally attractive and unstable.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 682127
zbMATH Keywords: generalized Liénard systems
zbMATH Keywords: center-focus
zbMATH Keywords: globally attractive
zbMATH Keywords: unstable
author: Maoan Han
reviewed by: Josef Hainzl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 682127