Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities

We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in IL2 completes...

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Detalhes bibliográficos
Autores: Itikawa, Jackson|||0000-0002-8268-0016, Llibre, Jaume|||0000-0002-9511-5999
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169461
Acesso em linha:https://ddd.uab.cat/record/169461
https://dx.doi.org/urn:doi:10.3934/dcdsb.2016.21.121
Access Level:acceso abierto
Palavra-chave:Phase portrait
Poincaré disk
Polynomial vector field
Uniform isochronous center
Descrição
Resumo:We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in IL2 completes the classification of the global phase portraits in the Poincar\'e disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.