Rational limit cycles of Abel equations
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))

Date:	2021
Abstract:	In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens. Moreover, we provide examples of these Abel equations with three nontrivial rational limit cycles. We also prove that in this case the limit cycles cannot be hyperbolic.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycles ; Rational limit cycles ; Abel equations ; Hyperbolic limit cycles
Published in:	Communications on pure & applied analysis, Vol. 20, Issue 3 (March 2021) , p. 1077-1089, ISSN 1553-5258

DOI: 10.3934/CPAA.2021007

Postprint 14 p, 670.7 KB

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