Um estudo qualitativo do contraexemplo de Pinchuk

Abstract

In this work we studied the topological behaviour of the level curves of the polinomial p of Pinchuk counterexample of the Real Jacobian Conjecture, namely, a polinomial non injective map of R^2 with the form (p,q) with a nonvanishing Jacobian Matrix determinant, using techniques of the qualitative theory of differential equations. We also found a family of polinomial functions witch are counterexamples of the Real Jacobian conjecture.