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Introduction

The most popular method for estimating the dimension of an attractor is due to Grassberger and Procaccia [Grassberger and Procaccia, 1983b] and Takens [Takens, 1983]. It comprises the calculation of the ``correlation integral''; the reason why it is called this way can be found in [Grassberger and Procaccia, 1983b]. The method was originally designed for estimating the ``correlation exponent'' or ``correlation dimension''. It has been generalized for estimating the dimension and entropy spectra [Pawelzik and Schuster, 1987]. In the following two sections, we show how this is done. In section 4.4 we give two analytic examples that broaden our understanding of the method and the shortcomings of such methods in general.



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