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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Bibliographic Details
Authors: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Format: article
Publication Date:2018
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:199331
Online Access:https://ddd.uab.cat/record/199331
https://dx.doi.org/urn:doi:10.1007/s10114-017-5478-y
Access Level:Open access
Keyword:Complex ellipse
Invariant algebraic curves
Phase portrait
Quadratic system
Description
Summary: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.