Propagation of microsupport at a hyperbolic fixed point.

Let p be a Hamiltonian and P its semiclassical quantization. To a hyperbolic fixed point of the Hamilton vector field Hp, an incoming stable manifold Л- and an outgoing stable manifold Л+ are associated. Microlocally near this point, we can consider a Cauchy problem for the equation Pu=zu (z is a spectral parameter), with data on Л-. The talk will be about the uniqueness of this Cauchy problem in the analytic category. In other words, we will consider if the incoming waves towards a non-degenerate maximum of the potential determine the outgoing waves.