PERIODIC-ORBITS IN POLYGONAL BILLIARDS

We review some properties of periodic orbit families in polygonal bill iards and discuss in particular a sum rule that they obey. In addition , we provide algorithms to determine periodic orbit families and prese nt numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we dea l with correlations in the length spectrum and find that long orbits d isplay Poisson fluctuations.