UNIVERSALITY IN THE LENGTH SPECTRUM OF INTEGRABLE SYSTEMS

The length spectrum of periodic orbits in integrable hamiltonian syste ms can be expressed in terms of the set of winding numbers {M1,...,M(f )} on the f-tori. Using the Poisson summation formula, one can thus ex press the density, SIGMAdelta(T - T(M)), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable pot entials, we explicitly show that the fluctuations are due to quantal e nergies. Further, their statistical properties are universal and typic al of a Poisson process as in the corresponding quantal energy eigenva lues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.