  The correlation dimension, that is, the dimension obtained by computing the
correlation function of pairs of points of a trajectory in phase space, is a
numerical technique introduced in the field of nonlinear dynamics in order to
compute the dimension of the manifold in which an orbit moves, without the need
of knowing the actual equations of motion that give rise to the trajectory.
This technique has been proposed in the past as a method to measure the
dimension of stellar orbits in astronomical potentials, i.e., the number of
isolating integrals of motion the orbits obey. Although the algorithm can in
principle yield that number, some care has to be taken in order to obtain good
results. We studied the relevant parameters of the technique, found their
optimal values, and tested the validity of the method on a number of potentials
previously studied in the literature, using the SALI, Lyapunov exponents and
spectral dynamics as gauges.
