The existence of chaotic dynamics has been known for a long time among mathematicians, starting with Poincare's work at the turn of the century and continuing with the subsequent pioneering studies of Birkhoff, Cartwright and Littlewood, Levinson, Smale, and Kolmogorov and his students. At first, knowledge of this work remained largely confined to the mathematical community. Starting in the mid-1970s, and stimulated by the availability of digital computers, this situation rapidly changed, as the broad impact and occurrence of chaos in the sciences and engineering began to be widely recognized. It has been demonstrated that chaos is relevant to problems in fields as diverse as ecology, chemistry, fluid mechanics, solid state devices, biology, and celestial mechanics.