Journal Article

Finding how many isolating integrals of motion an orbit obeys

D. D. Carpintero

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 388, issue 3, pages 1293-1304
Published in print August 2008 | ISSN: 0035-8711
Published online July 2008 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.13469.x
Finding how many isolating integrals of motion an orbit obeys

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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.

Keywords: stellar dynamics; methods: numerical; galaxies: kinematics and dynamics

Journal Article.  8092 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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