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We have described and to some extent justified a method to retrieve
geometrical information from a one-dimensional time series by
reconstructing a phase space picture of the attractor. Modifications
and extensions of this method which take into account the practical
problems of time series analysis have been discussed. It is important to
notice that there are many different approaches to these problems and
until now we do not have a general technique which can be applied to all
time series. Rather than that one has to choose the technique which seems
to be most appropriate for each individual data set.
Further improvements of the reconstructed attractor-picture are possible,
e.g. by using the tesselation method [13]. Having gone through the
embedding process one can use the well-known methods to quantify the
system by calculating the usual dimensions, Lyapunov exponents, etc. An
interesting application of the embedding technique is the prediction of a
dynamical system, using the information retrieved from a time series
[9,12,16].

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Martin_Engel
2000-05-25