A polynomial map F = (P,Q) ∈ ℤ[x,y]² with Jacobian $JF:=P_x{Q}_y-P_y{Q}_x\equiv 1$ has a polynomial inverse with integer coefficients if the complex plane curve P = 0 has infinitely many integer points.

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.