Assume an n-dimensional dynamical system 
evolving on an
attractor A. A has fractal dimension d, which often is
considerably smaller then n. The system state 
is
observed through a sequence of measurements 
,
resulting in a time series of measurements 
. Under weak assumptions concerning 
and the fractal embedding
theorem[9] ensures that, for 
, the
set of all delayed coordinate vectors
with an arbitrary delay time T, forms an embedding of A in the
DD-dimensional reconstruction space. We call the minimal DD,
which yields an embedding of A, the embedding dimension
. Because an embedding preserves characteristic features of
A, especially it is one to one, it may be employed for building a
system model. For this purpose the reconstruction of the attractor is
used to uniquely identify the systems state thereby establishing the
possibility of uniquely predicting the systems evolution. The
prediction function may be represented by a hyperplane over the
attractor in an (D+1) dimensional space. By iterating this
prediction function we obtain a vector valued system model which,
however, is valid only at the respective attractor.
For the reconstruction of instationary systems dynamics we confine
ourselves to the case of slowly varying parameters and model the
instationary system using a sequence of attractors.