A new qualitative proof of a result on the real jacobian conjecture

Abstract

Let F = (f, g) : ℝ 2 → ℝ 2 be a polynomial map such that det DF (x) is different from zero for all x ∈ ℝ 2. We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of (Formula presented) and (Formula presented), respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If (Formula presented) and (Formula presented) do not have real linear factors in common, then F is injective.