  We develop a scattering theory for perturbations of powers of the Laplacian
on asymptotically Euclidean manifolds. The (absolute) scattering matrix is
shown to be a Fourier integral operator associated to the geodesic flow at time
\pi on the boundary. Furthermore, it is shown that on \Real^n the asymptotics
of certain short-range perturbations of \Delta^k can be recovered from the
scattering matrix at a finite number of energies.
