Quadratic and cubic systems with degenerate infinity
type: Item
instance of: scholarly article
title: Quadratic and cubic systems with degenerate infinity
zbMATH Open document ID: 0851.34028
author: Armengol Gasull
author: Rafel Prohens
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-11-26T00:00:00Z
review text: The authors obtain an affine classification of quadratic systems with degenerate infinity in eight types and prove that they present 13 phase portraits on the Poincaré sphere. It seems that they did not know the classical paper of \textit{W. Buchel} [Mitt. Math. Ges. Hamburg 4, No. 4, 133-169 (1904)]. For cubic systems with degenerate infinity the authors show that there are examples of such systems with at least three concentric limit cycles; they also give a criterion to ensure that in some cases the number of such limit cycles is less than or equal to two.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 902484
zbMATH Keywords: affine classification of quadratic systems with degenerate infinity
zbMATH Keywords: phase portraits
zbMATH Keywords: Poincaré sphere
zbMATH Keywords: cubic systems
zbMATH Keywords: three concentric limit cycles
reviewed by: Yanqian Ye
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0065
OpenAlex ID: W2068506928
DOI: 10.1006/JMAA.1996.0065
description: scientific article; zbMATH DE number 902484