A sufficient condition in order that the real Jacobian conjecture in R2 holds

Abstract

Let F=(f,g):R2 → R2 be a polynomial map such that det DF(x, y) is different from zero for all (x,y) ∈ R2 and 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+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.