REGULARITY IN NONLINEAR DYNAMICAL-SYSTEMS

Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regu larities, to allow us to explain and predict the behavior of these sys tems. Using the driven simple pendulum as a paradigm, we identify thre e senses that regularity might have in connection with nonlinear dynam ical systems: periodicity, uniqueness, and perturbative stability. Suc h systems are always regular only in the second of these senses, and t hat sense is not robust enough to support predictions. We thus illustr ate precisely how physical laws in the classical regime of dynamical s ystems fail to exhibit predictive power.