CONICET | Buscador de Institutos y Recursos Humanos

The correlation dimension, that is, the dimension obtained by computing thecorrelation function of pairs of points of a trajectory in phase space, is anumerical technique introduced in the field of nonlinear dynamics in order tocompute the dimension of the manifold in which an orbit moves, without the needof knowing the actual equations of motion that give rise to the trajectory. Thistechnique has been proposed in the past as a method to measure the dimension ofstellar orbits in astronomical potentials, i.e., the number of isolatingintegrals of motion the orbits obey. Although the algorithm can in principleyield that number, some care has to be taken in order to obtain good results. Westudied the relevant parameters of the technique, found their optimal values,and tested the validity of the method on a number of potentials previouslystudied in the literature, using the SALI, Lyapunov exponents and spectraldynamics as gauges.