MAPPINGS WITH A COMPOSITE PART AND WITH A CONSTANT JACOBIAN

In this paper, we give a classification for mappings of the form f(x, y) = (x + u(p(x, y)), y + v(q(x, y))), u,v is an element of C[t], p,q is an element of C[x,y], i.e., mappings with a composite part, that sa tisfy the Jacobian hypothesis. This is done for those mappings for whi ch a certain ''no cancellation'' argument can be applied. The proof is rather technical, and strangely it relies on the study of the rationa l solutions of the so-called Burger's equation with no viscosity. This is a nonlinear scalar hyperbolic PDE that modelizes the behavior of g as with no viscosity. Originally, it served for street traffic model.