2008/05/16 by D. D. Carpintero, Daniel D. Carpintero
Engineering · Physics and Astronomy · #Chaos control and synchronization #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #astro-ph
paper · pdf · doi:10.1111/j.1365-2966.2008.13469.x
MN LaTeX style v2.2, 12 pages, 27 figures, 4 tables, to be published in MNRAS
arxiv created 2008/05/16 · openalex publication_date 2008/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 non-linear 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, that is 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 Smaller Alignment Index (SALI), Lyapunov exponents and spectral dynamics as gauges.