LAW OF PROLIFERATION OF PERIODIC-ORBITS IN PSEUDOINTEGRABLE BILLIARDS

We prove that the periodic-orbit counting function, a measure of the rate of proliferation of periodic orbits, for a barrier billiard and the pi/3-rhombus billiard is of the form ax2 + bx + c, where x is the length (equivalently, period) up to which periodic orbits are counted and a,b,c are system-specific constants. The generality of our arguments strongly suggests that the law of proliferation given here is a representation of general truth about two-dimensional plane-polygonal billiards.