Evaluation of dimensions and entropies of chaotic systems

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Abstract
Accurate evaluations of fractal dimensions are limited by intrinsic properties of strange attractors (lacunarity, nonuniformity) and by statistical effects (finite number of data points). The application of the fixed-mass (nearest-neighbor distance) method is studied in view of these limitations, showing that the method is also well suited for the measurement of large dimensions. The tuning of the algorithm and the problems inherent in the analysis of experimental systems (small number of data points, noise, and drifts) are analyzed with reference to several computer experiments. The evaluation of the metric entropies of experimental signals by means of the same algorithm is discussed.

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