Edward Ott
Department of Electrical and Computer Engineering
University of Maryland, College Park
Riddled Basins of Attraction of Chaotic Systems: Inevitable uncertainties in the outcomes of experiments
In certain situations, it is possible for the dynamical behavior of chaotic systems to be such that even the qualitative character of the eventual long time motion (i.e., the attractor) may be uncertain. In particular, it is possible that for every initial condition yielding a given type of behavior there exist arbitrarily small perturbation from that initial condition that can yield a qualitatively different behavior. Thus the repeatability of even qualitative outcomes of experiments for such systems comes into question. This phenomenon is due to a "riddled" basin of attraction. (A basin of attraction is the set of initial conditions in state space that yield a particular long time motion). This talk will discuss riddle basins in elementary terms, and will give illustrative numerical and analytical examples.