Center cyclicity of a family of quartic polynomial differential system

In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove t...

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Detalles Bibliográficos
Autores: García, Isaac|||0000-0001-6982-9632, Llibre, Jaume|||0000-0002-9511-5999, Maza, Susanna|||0000-0001-9488-5644
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169476
Acceso en línea:https://ddd.uab.cat/record/169476
https://dx.doi.org/urn:doi:10.1007/s00030-016-0388-8
Access Level:acceso abierto
Palabra clave:Algebraic limit cycles
Bautin ideal
Center
Cyclicity
Polynomial vector fields
Descripción
Sumario:In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.