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** Contents**

In this chapter and the two following ones we will discuss two methods for
estimating the dimension and entropy spectra from a time series.
Both methods use information from distances between points in
phase space. Nearest neighbour methods are based on a fixed number
of distances within a ball around reference points.
The dimension and entropy spectra can be estimated using an expression
for the expectation of the powers of the distance to the -th nearest
neighbour of a reference point.
In the next section, we show how such an expression can be
derived. The result can be used in several ways to obtain
estimators for the dimension function; these options are discussed
in section 3.3.
In section 3.4 we demonstrate how to use the nearest-neighbour
algorithm with the Rössler attractor.
Finally, we briefly describe the current implementation
of the estimator algorithms in section 3.5.

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