Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant

Electronic Journal of Differential Equations

article

Jaume Llibre¹  Regilene D. S. Oliveira³  Camila A. B. Rodrigues⁴ 

[1] Departament de Matematiques Universitat Aut7oacute;noma de Barcelona 08193 Bellaterra;Instituto de Ci\ências Matemáticas e Computação Universidade de São Paulo Avenida Trabalhador São-carlense;Departamento de Matemática Universidade Federal de Santa Catarina

关键词: Quadratic vector fields;    algebraic invariant curve;    Darboux invariant;    global phase portrait.Show me the PDF file (1190 KB);    TEX file for this article.;   

DOI  :  10.58997/ejde.2021.69

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

Let QS be the class of non-degenerate planar quadratic differential systemsand 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 ofthe phase portraits in QS3 having a Darboux invariant of the form f(x, y)est, with s in R.

【 授权许可】

CC BY