Estrutura topológica do retrato de fase para campos vetoriais lineares em R3 e aplicações

Abstract

In 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.