Contribution of periodic diffractive geodesics

On an euclidean surface with conical singularities, the wave-trace is expected to be singular at L where L is the length of some diffractive periodic geodesic. In this paper, we compute the leading term of the singularity brought to the trace by a regular, isolated diffractive geodesic and by a regular family of periodic non-diffractive geodesic. These results can be applied to polygons.