| Texto completo | |
| Autor(es): |
Oliveira, Regilene D. S.
;
Rezende, Alex C.
;
Schlomiuk, Dana
;
Vulpe, Nicolae
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Electronic Journal of Qualitative Theory of Differential Equations; v. N/A, n. 60, p. 105-pg., 2025-01-01. |
| Resumo | |
Denote by QS the class of all non-degenerate planar quadratic differential systems and by QSP the subclass of QS of all systems possessing at least one invariant parabola. In this paper we consider the subfamily of QSP defined by the condition eta not equal 0, which means the presence of three distinct infinite singularities real or complex. We denote this subfamily by QSP(eta not equal 0). We investigate all possible configurations of invariant parabolas and invariant straight lines which systems in QSP(eta not equal 0) could possess and their geometric properties encoded in such configurations. The classification presented here is taken modulo the action of the group of real affine transformations and time rescaling and it is given in terms of affine invariant polynomials. It yields a total of 144 distinct configurations. The obtained classification is an algorithm which makes it possible for any given real quadratic differential system in QSP( eta not equal 0) to specify its configuration of invariant parabolas and straight lines. This work will prove helpful in studying the integrability of the systems in QSP(eta not equal 0). (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 |
| Processo FAPESP: | 24/13454-4 - Investigação de sistemas diferenciais polinomiais: classificação, bifurcações e aplicações |
| Beneficiário: | Alex Carlucci Rezende |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |