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The Kolmogorov entropy [Kolmogorov, 1959]
is a measure for the rate at which
information about the state of the system is lost in the course of time.
It is
defined as follows [Schuster, 1988]. Suppose again that the dimensional
phase space is
partitioned into boxes of size . Let
be the
joint probability that is in box , ..., and
is in box . Then

(2.4) 
where is the time interval between measurements on
the state of the system; for maps, and the limit
is omitted.
The entropy can be used to classify dynamical systems, since
is zero for regular motion, it is infinite in random systems,
but it is finite and positive in chaotic systems, see
[Schuster, 1988, p.112].
The definition has been generalized to the
spectrum [Schuster, 1988,Renyi, 1970]:

(2.5) 
The function is also monotonically decreasing with .
The is called the topological entropy;
the is the metric or KolmogorovSinai entropy,
and the is called the ``correlation entropy''.
In this report we will focus on the estimation of the .
A is a sufficient condition for chaos since
[Grassberger and Procaccia, 1983a].
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