Centro global e o problema da injetividade global no plano

Abstract

The Real Jacobian Conjecture in the plane says that a polynomial map of the plane in the plane with non-zero Jacobian is one-to-one. We know that this conjecture is false in general. But, it is of great interest to nd classes of maps satisfying the hypotheses in which the conjecture is true. In this work, we present a way to study this problem using the qualitative theory of di erential equations. More speci cally, we will see the connection between the Real Jacobian Conjecture in the plane and the existence of a global center of a Hamiltonian vector eld.