Retratos de fase de uma família de sistemas quadráticos planares integráveis com duas parábolas invariantes

Abstract

In this work we prove the Grobman-Hartman Theorem and the Local Stable Manifold Theorem, classical results in the study of the local behavior of the solutions of nonlinear differential equations. Then we provide the global phase portrait in the Poincaré disc of all quadratic planar differential systems with two invariant parabolas given by equations f1 = 0, f2 = 0 and a first integral of the form H = f 1 f 2 , where , are real constants.