History

  • Nonlinear oscillators and applications in physics and engineering. Played a vital role in the development of such technologies as radio, radar, phase-locked loops, and lasers.

  • High-speed computers ⇒ Lorenz’s discovery in 1963 of chaotic motion on a strange attractor

  • emergence of chaos theory. applications in fluids, chemical reactions, electronic circuits, mechanical oscillators, and semiconductors.

  • Mandelbrot’s set & fractals

  • Mathematical biology ⇒ biological oscillations, especially circadian rhythms and heart rhythms

Importance

  • differential equations & iterated maps (difference equations)