LENGTH SPECTRUM OF CHAOTIC BILLIARDS

We derive here an expression for the length spectrum, SIGMAdelta(l - l (j)) of periodic orbits in chaotic billiards. Our analysis yields the average exponential proliferation of lengths superimposed by fluctuati ons which arise as a sum over contributions from ''quantal energies.'' We further show that these fluctuations are non-Poisson. Long orbits, however, mimic the Poisson result for the spectral rigidity, DELTA(L) .