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 $\pi b_0l^2/\langle a(l) \rangle$,where$b_0$isaconstantand$\langle a(l) \rangle$istheaverageareaoccupiedbythesefamilies\mathrm{.}Wealsofindthat$\langle a(l) \rangle$increaseswith$l$ 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.