Finding invariant tori in the problem of a periodically corrugated waveguide

some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. the dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. we show that the phase space is mixed in the sense that there are kam islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. we have used a connection with the standard mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.