  Solutions of semi-classical Schrodinger equation with isotropic harmonic
potential focus periodically in time. We study the perturbation of this
equation by a nonlinear term. If the scaling of this perturbation is critical,
each focus crossing is described by a nonlinear scattering operator, which is
therefore iterated as many times as the solution passes through a focus. The
study of this nonlinear problem is made possible by the introduction of two
operators well adapted to Schrodinger equations with harmonic potential, and by
suitable Strichartz inequalities.
