A new qualitative proof of a result on the real Jacobian conjecture.

Let F= (f, g) : R2 → R2 be a polynomial map such that det DF(x) is different from zero for all x ∈ R2. We assume that the degrees of f and g are equal. We denote by f and G the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If f and g do not have real linear factors in common, then F is injective.