QUADRATIC SYSTEMS WITH AN INVARIANT ALGEBRAIC CURVE OF DEGREE 3 AND A DARBOUX INVARIANT

Autor(es)

Llibre, Jaume ^[1] ; Oliveira, Regilene D. S. ^[2] ; Rodrigues, Camila A. B. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Fed Santa Catarina, Dept Matemat, BR-88040900 Florianopolis, SC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Electronic Journal of Differential Equations; AUG 16 2021.
• Citações Web of Science: 0

Resumo

Let QS be the class of non-degenerate planar quadratic differential systems and QS(3) 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 QS(3). Working with these normal forms we complete the characterization of the phase portraits in QS(3) having a Darboux invariant of the form f(x, y)e(st), with s is an element of R. (AU)

• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático