Algebraic limit cycles on quadratic polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)

Date:	2018
Abstract:	Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: Quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that for a quadratic polynomial differential system having an invariant algebraic curve with at most one pair of diametrally opposite singular point at infinity, has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture.
Grants:	European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycles ; Quadratic polynomial differential system ; Quadratic polynomial vector field
Published in:	Proceedings of the Edinburgh Mathematical Society, Vol. 61, issue 2 (May 2018) , p. 499-512, ISSN 1464-3839

DOI: 10.1017/S0013091517000244

Postprint 13 p, 721.0 KB

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