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Comptes Rendus Mathématique
Volume 357, n° 2
pages 143-166 (février 2019)
Doi : 10.1016/j.crma.2018.12.008
Received : 19 November 2018 ;  accepted : 16 December 2018
Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line
Portraits de phase de systèmes quadratiques intégrables avec une parabole et une ligne droite invariantes
 

Jaume Llibre a , Maurício Fronza da Silva b
a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain 
b Departamento de Matemática, Universidade Federal de Santa Maria, 97110-820, Santa Maria, RS, Brazil 

Abstract

We classify the phase portraits of the quadratic polynomial differential systems having an invariant parabola, an invariant straight line, and a Darboux first integral produced by these two invariant curves.

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Résumé

Nous classifions les portraits de phase des systèmes différentiels polynomiaux quadratiques ayant une parabole invariante, une ligne droite invariante et une intégrale première de Darboux produite par ces deux invariants.

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