Chaotic experimental systems are often investigated using delay coordinates. Estimated values of the correlation dimension in delay coordinate space typically increase with the number of delays and eventually reach a plateau (on which the dimension estimate is relatively constant) whose value is commonly taken as an estimate of the correlation dimension ${\mathit{D}}_2$ of the underlying chaotic attractor. We report a rigorous result which implies that, for long enough data sets, the plateau begins when the number of delay coordinates first exceeds ${\mathit{D}}_2$. Numerical experiments are presented. We also discuss how lack of sufficient data can produce results that seem to be inconsistent with the theoretical prediction.

• Received 22 February 1993

DOI:https://doi.org/10.1103/PhysRevLett.70.3872