A sufficient condition in order that the real Jacobian conjecture in R2R2 holds

Let F=(f,g):R2→R2F=(f,g):R2→R2 be a polynomial map such that det⁡DF(x,y)det⁡DF(x,y) is different from zero for all (x,y)∈R2(x,y)∈R2 and F(0,0)=(0,0)F(0,0)=(0,0). We prove that for the injectivity of F   it is sufficient to assume that the higher homogeneous terms of the polynomials ffx+ggxffx+ggx and ffy+ggyffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.