In chaos theory, the correlation integral is the mean probability that the states at two different times are close:

a norm (e.g. Euclidean norm the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem):

the time delay.

The correlation integral is used to estimate the correlation dimension.

An estimator of the correlation integral is the correlation sum:

See also

• Recurrence quantification analysis

References

• http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983PhyD....9..189G