2025-12-302025-12-302025SILVA, Luan Lima da; TONON, Durval José. Estrutura topológica do retrato de fase para campos vetoriais lineares em R3 e aplicações. Revista Eletrônica Paulista de Matemática, Bauru, v. 26, e26007, 2025. DOI: 10.21167/cqdv26e26007. Disponível em: https://revistas.bauru.unesp.br/index.php/revistacqd/pt_BR/article/view/484. Acesso em: 9 dez. 2025.e- 2316-9664https://repositorio.bc.ufg.br//handle/ri/29237In this paper, we present an analysis of the sign of the real part of the roots of a polynomial of degree 3 as a function of its co- efficients. The problem will be approached from an analytical point of view, knowing that from an algebraic point of view the problem has already been dealt with in the literature without significant advances. As an application of the results obtained, we fully characterize the dynamics and topological structure of the phase portrait for linear fields in R3. In addition, we present applications in the local qualitative study of equilibrium points for vector fields in R3 defined from one or more parameters.porAcesso Abertohttp://creativecommons.org/licenses/by-nc-nd/4.0/Three-dimensional linear vector fieldsRoots of cubic polynomialsLocal dynamics near to equilibrium pointsBifurcation diagramCampos de vetores lineares tridimensionaisRaízes de polinômios cúbicosDinâmica local próximo de pontos de equilíbrioDiagrama de bifurcaçõesArtigo10.21167/cqdv26e26007