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

Agraïments: FEDER-UNAB 10-4E-378. The two authors are also supported by a CAPES CSF-PVE grant 88881. 030454/ 2013-01 from the program CSF-PVE.Let F = (f, g) : R → R 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 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.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 injectiv