A new characterization of the invertibility of polynomial maps
  In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the invertibility of F as well as a formula for the inverse of F in terms of these finite sequences of polynomials. Some examples illustrate the effective aspects of our approach. 
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo and Zbigniew Hajto
math.AC