On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity

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 hav...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:182533
Acceso en línea:https://ddd.uab.cat/record/182533
https://dx.doi.org/urn:doi:10.1007/s10711-017-0244-y
Access Level:acceso abierto
Palabra clave:Algebraic limit cycles
Quadratic polynomial differential system
Quadratic polynomial vector field
Descripción
Sumario: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.