Evolution of ‘Chaos’ Theory
The Breakthrough came with the work of Poincare in the late 1980’s. He introduced a new point of view that emphasized qualitative rather than quantitative questions. Poincare developed a powerful approach for analyzing such questions. That approach has flowered into the modern subject of dynamics, with applications reaching far beyond celestial machines. Poincare was the first person to glimpse the possibility of “CHAOS”, in which a deterministic system exhibits a-periodic behavior that depends sensitively on the initial conditions, thereby rendering long-term prediction impossible.
But chaos remained in the background in the first half of this century; instead dynamics was largely concerned with nonlinear oscillators and their applications in physics and engineering. Nonlinear oscillators played a vital role in the development of such technologies as radio, radar, phase-locked loops, and lasers. On the theoretical side, nonlinear oscillators also stimulated the invention of new mathematical technique.