Limit sets of dynamical systems
type: Item
instance of: scholarly article
title: Limit sets of dynamical systems
zbMATH Open document ID: 1016.37013
DOI: 10.1023/A:1017981118874
author: O. V. Zubova
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The following result is proved: Assume that a system of autonomous ordinary differential equations \(dX/dt=f(x)\) is defined for all \(x\in \mathbb{R}^n\) with continuous function \(f\) and has two limit cycles \(M_\omega\) and \(M_\alpha\), which are Lyapunov asymptotically stable as \(t\to\infty\) and \(t\to -\infty\), respectively. The set of points, asymptotic as \(t\to\infty\) to \(M_\omega\) and as \(t\to -\infty\) to \(M_\alpha\) is invariant, connected and open.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1915974
zbMATH Keywords: switching
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: limit set
zbMATH Keywords: invariant set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1915974