CHAOTIC BILLIARDS WITH NEUTRAL BOUNDARIES

This paper establishes the conditions under which rational billiards, i.e., billiards moving within polygons whose vertex angles are all rat ional multiples of pi, exhibit a chaos that is empirically indistingui shable from that of systems traditionally called chaotic. Specifically , we show empirically that these systems can have positive Liapunov nu mber, positive metric entropy, and positive algorithmic complexity. Al though our results appear to contradict rigorous mathematical assertio ns precluding chaos in rational billiards, such is not the case. In a real sense, rational billiards emphasize the quite practical, physical distinction which exists between continuum and finite mathematics.