Predicting the dimension of strange attractors

Abstract

The correlation dimension was calculated for a collection of 6080 strange attractors obtained numerically from low-degree polynomial, low-dimensional maps and flows. It was found that the average correlation dimension scales approximately as the square root of the dimension of the system with a surprisingly small variation. This result provides an estimate of the number of dynamical variables required to characterize an experiment in which a strange attractor has been found as well as an estimate of the dimension of attractors produced by chaotic systems in which the dimension of the state space is known.