Global phase portraits of quadratic systems with a complex ellipse as invariant algebraic curve

In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve. We provide all the different topolo...

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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:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:199331
Acceso en línea:https://ddd.uab.cat/record/199331
https://dx.doi.org/urn:doi:10.1007/s10114-017-5478-y
Access Level:acceso abierto
Palabra clave:Complex ellipse
Invariant algebraic curves
Phase portrait
Quadratic system
Descripción
Sumario:In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincaré disc.