Periodic orbits and spectral statistics of pseudointegrable billiards

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than l increases as pi b(0)l(2)/[a(l)], where b(0) is a constant and [a(l)] is the average area occupied by these families. We also find that [a(l)] increases with I before saturating. Finally, we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies.