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Introduction

It has been shown that deterministic dynamical systems may exhibit erratic or ``chaotic'' behaviour. Our aim is to gain knowledge of such a system from an experimental time series. Of course it would be most desirable to determine the ``equations of motion'' (see e.g. [Cremers and Hübler, 1987]). However, in this report we restrict ourselves to the estimation of two fundamental properties of chaotic systems viz. the dimension and entropy spectra of their attractors. In the following sections, we give the mathematical definitions of the generalized dimensions and entropies. Furthermore, we will show that they can in principle be estimated from a scalar time series. For a more thorough treatment we refer to e.g. Ref. [Eckmann and Ruelle, 1985].



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