PERIODIC TRAJECTORIES IN RIGHT-TRIANGLE BILLIARDS

Billiard problems are simple examples of Hamiltonian dynamical systems . These problems have been used as model systems to study the link bet wen classical and quantum chaos. The heart of this linkage is provided by the periodic orbits in the classical system. In this article we wi ll show that for an arbitrary right triangle, almost all trajectories that begin perpendicular to a side are periodic, that is, the set of p oints on the sides of a right triangle from which nonperiodic (perpend icular) trajectories begin is a set of measure zero. Our proof incorpo rates the previous result for rational right triangles (where the angl es are rational multiples of pi), while extending the result to nonrat ional right triangles.