Jaume Llibre, Regilene D. S. Oliveira, Camila A. B. Rodrigues
Abstract:
Let QS be the class of non-degenerate planar quadratic differential systems
and QS3 its subclass formed by the systems possessing an invariant
cubic f(x,y)=0. In this article, using the action of the group of real affine
transformations and time rescaling on QS, we obtain all the possible normal
forms for the quadratic systems in QS3.
Working with these normal forms we complete the characterization of
the phase portraits in QS3 having a Darboux invariant of the form
f(x, y)est, with s in R.
Submitted September 25, 2020. Published August 16, 2021.
Math Subject Classifications: 34C05, 34A34, 34C23.
Key Words: Quadratic vector fields; algebraic invariant curve; Darboux invariant;
global phase portrait.
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DOI: https://doi.org/10.58997/ejde.2021.69
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Jaume Llibre Departament de Matematiques Universitat Aut7oacute;noma de Barcelona 08193 Bellaterra, Barcelona, Catalonia, Spain email: jllibre@mat.uab.cat |
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Regilene D. S. Oliveira Instituto de Ci\ências Matemáticas e Computação Universidade de São Paulo Avenida Trabalhador São-carlense, 400, 13.560-970 São Carlos, SP, Brazil email: regilene@icmc.usp.br |
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Camila A. B. Rodrigues Departamento de Matemática Universidade Federal de Santa Catarina, 88040-900 Florianópolis, Santa Catarina, Brazil < email: c.r.lima@ufsc.br |
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