Abstract
This paper establishes the conditions under which rational billiards, i.e., billiards moving within polygons whose vertex angles are all rational multiples of π, exhibit a chaos that is empirically indistinguishable from that of systems traditionally called chaotic. Specifically, we show empirically that these systems can have positive Liapunov number, positive metric entropy, and positive algorithmic complexity. Although our results appear to contradict rigorous mathematical assertions 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.
- Received 5 August 1993
DOI:https://doi.org/10.1103/PhysRevE.48.3414
©1993 American Physical Society