Algebraic limit cycles for quadratic polynomial differential systems
type: Item
instance of: scholarly article
title: Algebraic limit cycles for quadratic polynomial differential systems
zbMATH Open document ID: 1426.34040
author: Jaume Llibre
author: Claudia Valls
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-12-18T00:00:00Z
review text: The paper deals with the question about the maximal number of algebraic limit cycle as a weakened version of the second part of Hilbert's 16th problem. For quadratic planar autonomous systems the conjecture is well-known that such systems have at most one algebraic limit cycle. The authors provide a positive answer to this conjecture in a new case when the quadratic system has three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, in other words, the Jacobian matrix of the differential equation at each of these points has two eigenvalues \(\lambda \neq 0\), \(\mu \neq 0\) such that \(\lambda/\mu \) is not a positive rational number.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 6994970
zbMATH Keywords: algebraic limit cycle
zbMATH Keywords: quadratic polynomial differential system
zbMATH Keywords: Hilbert's 16th problem
MaRDI profile type: Publication
full work available at URL: dcdsb.2018070
OpenAlex ID: W2781883148
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DOI: 10.3934/DCDSB.2018070
description: scientific article; zbMATH DE number 6994970