Jaume Llibre, Jiang Yu
Abstract:
In this article we study a class of integrable quadratic systems
and classify all its phase portraits. More precisely, we
characterize the class of all quadratic polynomial differential
systems in the plane having an ellipse and a straight line as
invariant algebraic curves. We show that this class is integrable
and we provide all the different topological phase portraits that
this class exhibits in the Poincare disc.
Submitted September 4, 2015. Published December 24, 2015.
Math Subject Classifications: 34C05.
Key Words: Quadratic system; first integral; global phase portraits;
invariant ellipse; invariant straight line.
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Jaume Llibre Departament de Matemátiques Universitat Autónoma de Barcelona 08193 Bellaterra, Barcelona, Catalonia, Spain email: jllibre@mat.uab.cat | |
Jiang Yu Department of Mathematics Shanghai Jiao Tong University Shanghai 200240, China email: jiangyu@sjtu.edu.cn |
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