On R. A. Smith's autonomous convergence theorem
type: Item
instance of: scholarly article
title: On R. A. Smith's autonomous convergence theorem
zbMATH Open document ID: 0841.34052
author: Michael Y. Li
author: James S. Muldowney
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-07-21T00:00:00Z
review text: The authors study the autonomous system \(x'= f(x)\) on a domain \(D\) in \(\mathbb{R}^n\). They are concerned with the \(\alpha\)- and \(\omega\)-limit sets and develop sufficient conditions that these consist only of equilibria. In addition, they give sufficient conditions that any invariant set have Hausdorff dimension \(\leq 1\).
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C30
zbMATH DE Number: 796927
zbMATH Keywords: Bendixson's criterion
zbMATH Keywords: Dulac criterion
zbMATH Keywords: center manifold
zbMATH Keywords: wandering points
zbMATH Keywords: autonomous system
zbMATH Keywords: \(\alpha\)- and \(\omega\)-limit sets
zbMATH Keywords: invariant set
zbMATH Keywords: Hausdorff dimension
reviewed by: Alan R. Hausrath
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072289
OpenAlex ID: W2042371484
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DOI: 10.1216/RMJM/1181072289
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description: scientific article; zbMATH DE number 796927