Notions of order and chaos go back a long way. The Greeks held that all motion could be decomposed into "perfect" circular motions, and this belief led to the theory of planetary epicycles. We might phrase the Platonic ideal this way: all motion is quasiperiodic, meaning the Fourier transform of any coordinate consists of sharp spikes (Fig. 1). Poincaré near the turn of the century, was perhaps the first person to realize that there are (bounded) motions whose spectra do not have this form. Such systems have a broadband, continuous component in their spectra, as shown in Fig. 2.
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