Eulerian systems of partial differential equations and the Jacobian conjecture (Q1181494)

A new approach to the jacobian conjecture is presented. The authors generalize the jacobian conjecture to a much more general one (Eulerian conjecture) from the field of polynomial mappings to the field of polynomial differential mappings (the latter are differential operators with polynomial coefficients). They define a subclass of these mappings (Eulerian systems) and formulate the Eulerian conjecture in terms of it. They prove that the Eulerian conjecture implies the jacobian conjecture and that for a polynomial mapping with non-zero constant jacobian the condition of being ``eulerian'' implies its invertibility.