The per iod of an oscillator tells us much about its structure. J. J. Thomson's deduction that a particle with the e/rn of an electron was in the atom is perhaps the most stunning instance. For us, the deduction of the mean density of a star from its oscillation period is another important example. What then can we deduce about an oscillator that is not periodic? If there are several frequencies or if the behavior is chaotic, may we not hope to learn even more delicate vital statistics about its workings? The recent progress in the theory of dynamical systems, particularly in the elucidat ion...