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Time Series Analysis
A Part III Essay
Ulf Martin Engel
Darwin College
Cambridge CB3 9EU
United Kingdom
1 May 1991
(second, improved version: 15 November 1991)
Abstract:
It is possible to reconstruct from a one-dimensional time series
(obtained by an experiment or numerically) the attractor of the
corresponding dynamical system. The technique used for this
purpose, the method of delays, is described, a theoretical
justification (using an embedding trick)
is given and the problems one encounters when
implementing this technique in practice are discussed. The
importance of the method of delays lies in the fact that, in
principle, it enables us to retrieve ``all'' the characteristic
quantities of a (strange) attractor from the time series, no matter
how complicated the structure of the attractor is, despite of the
simple form of the data.
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2000-05-25