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We derive semiclassical contributions of periodic orbits from a boundaryintegral equation for three-dimensional billiard systems. We use an iterativemethod that keeps track of the composition of the stability matrix and theMaslov index as an orbit is traversed. Results are given for isolated periodicorbits and rotationally invariant families of periodic orbits in axiallysymmetric billiard systems. A practical method for determining the stabilitymatrix and the Maslov index is described.Comment: LaTeX, 19 page

Billiard systems in three dimensions: the boundary integral equation and the trace formula