Resumen:
The Real Jacobian Conjecture (RJC) states that a polynomial map of the plane in the
plane with nonzero Jacobian at every point is invertible. Although we know that this
conjecture is false, it is of great interest to find conditions that guarantee the global
invertibility of local diffeomorphisms, in particular, of polynomial maps in the plane. In
this dissertation, we explore results related to the RJC, with emphasis on results based on
the Qualitative Theory of Ordinary Differential Equations. In particular, we explore the
relation between global injectivity and topological equivalence of parallel vector fields.
