A GEOMETRICAL APPROACH TO WAVE DYNAMICS IN BILLIARDS

A semi-classical time-dependent Green's function for the hyperbolic wa ve equation is constructed using a summation over quasi-recurrent clas sical ray trajectories. The finite resolution of the wave problem asso ciated to the smallest wavelength introduces a natural coarse graining which allows us to partition the classical rays into bundles. Our par ametrization introduces precursor contributions in the sum, which allo w for a very good agreement with the direct numerical integration of t he wave equation in integrable as well as chaotic two-dimensional (2D) billiards. These precursors give a new insight in the role of focal p oints in semi-classical wave dynamics.