Rational limit cycles of Abel equations
type: Item
instance of: scholarly article
title: Rational limit cycles of Abel equations
zbMATH Open document ID: 1471.34062
author: Jaume Llibre
author: Claudia Valls
published in: Communications on Pure and Applied Analysis
publication date: 2021-06-16T00:00:00Z
review text: The study deals with Abel equations \[\frac{dy}{dx}=A(x)y^2+B(x)y^3,\] where \(x \in [0, 1]\) and \(y\) are real variables and \(A(x)\) and \(B(x)\) are polynomials. The authors prove that these Abel equations can have at most two rational limit cycles, that is, cycles representable in the form \(y(x)=q(x)/p(x)\), where \(p\) and \(q\) are coprime polynomials. This bound can be reached with nonhyperbolic limit cycles. Moreover, examples of these Abel equations with two nontrivial rational limit cycles are derived.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C08
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7359937
zbMATH Keywords: algebraic limit cycles
zbMATH Keywords: rational limit cycles
zbMATH Keywords: Abel equations
MaRDI profile type: Publication
full work available at URL: cpaa.2021007
OpenAlex ID: W3122719515
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DOI: 10.3934/CPAA.2021007
description: scientific article; zbMATH DE number 7359937