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

Abstracts

Let F = (f, g) : R² → R²be 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 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 do not have real linear factors in common, then F is injective.

Real Jacobian conjecture; global injectivity; center; Poincaré compactification