On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)

Date:	2017
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 two pairs of diametrally opposite equilibrium points at infinity, has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2016-77278-P
Note:	Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycles ; Quadratic polynomial differential system ; Quadratic polynomial vector field
Published in:	Geometriae dedicata (Dordrecht), Vol. 191 (2017) , p. 37-52, ISSN 1572-9168

DOI: 10.1007/s10711-017-0244-y

Postprint 17 p, 722.0 KB

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