Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line

Jaume Llibre; Maurício Fronza da Silva

doi:10.1016/j.crma.2018.12.008

Ordinary differential equations

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]

Présenté par : the Editorial Board

Jaume Llibre ¹ ; Maurício Fronza da Silva ²

¹ Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
² Departamento de Matemática, Universidade Federal de Santa Maria, 97110-820, Santa Maria, RS, Brazil

Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 143-166.

Résumé
Abstract

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.

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.

Reçu le : 2018-11-19
Accepté le : 2018-12-16
Publié le : 2019-01-31

DOI : 10.1016/j.crma.2018.12.008

Affiliations des auteurs :

Jaume Llibre ¹ ; Maurício Fronza da Silva ²

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     author = {Jaume Llibre and Maur{\'\i}cio Fronza da Silva},
     title = {Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {143--166},
     publisher = {Elsevier},
     volume = {357},
     number = {2},
     year = {2019},
     doi = {10.1016/j.crma.2018.12.008},
     language = {en},
}

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Jaume Llibre; Maurício Fronza da Silva. Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 143-166. doi : 10.1016/j.crma.2018.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.12.008/

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