APPLICATION OF DIMENSION ALGORITHMS TO EXPERIMENTAL CHAOS

An important application of the theory of nonlinear dynamics is the analysis of erratic experimental data. We give a review of some recent developments in the methods and problems related to the estimation of the fractal dimension of a time-series. We discuss a series of conditions which should be fulfilled for serious dimension calculations and apply these methods to data from multiperiodic signals and from (pseudo stochastic) random walks in one dimension. We show how for limited data sets finite size effects can modify the observed values of the dimension and estimate the minimal number of data points required for a given sampling frequency in order to determine the attractor dimension.