Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2 |
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| Authors: | Laurent Cairó Jaume Llibre |
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| Institution: | 1. MAPMO/CNRS-Departement de Mathématiques. Université d’Orleans, 45067 Orléans, Cedex 2, France;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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| Abstract: | We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense. |
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| Keywords: | primary 34C05 34A34 34C14 |
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