A SCALING TEST FOR CORRELATION DIMENSIONS

A quantitative test is presented to check scaling and convergence of the correlation integral and consistency of two different algorithms. An application to two known attractors demonstrates that it allows one to judge fast and reliably the quality of a conjectured scaling behaviour above all in the case of short or noisy data. Results concerning minimum data amount and maximum noise level confirm earlier work, the crucial parameter concerning data length turns out, however, to be not the number of points, but the number of cycles in phase space (peaks in the time series).