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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