What is a Strange Attractor?
Before Chaos (BC?), the only known attractors (see [2.8]) were fixed points, periodic orbits (limit cycles), and invariant tori (quasiperiodic orbits). In fact the famous Poincaré-Bendixson theorem states that for a pair of first order differential equations, only fixed points and limit cycles can occur (there is no chaos in 2D flows). In a famous paper in 1963, Ed Lorenz discovered that simple systems of three differential equations can have complicated attractors. The Lorenz attractor (with its butterfly wings reminding us of sensitive dependence (see [2.10])) is the “icon” of chaos http://kong.apmaths.uwo.ca/~bfraser/version1/lorenzintro.html. Lorenz showed that his attractor was chaotic, since it exhibited sensitive dependence. Moreover, his attractor is also “strange,” which means that it is a fractal (see [3.2]). The term strange attractor was introduced by Ruelle and Takens in 1970 in their discussion of a scenario for the onset of turbulence in fluid flow. They noted that when
