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The regular or chaotic character of orbits of stars moving in the meridionalplane (R,z) of an axially symmetric elliptical galaxy with a dense, massivespherical nucleus and a dark matter halo component is under investigation. Inparticular, we explore how the flattening of an elliptical galaxy influencesthe overall orbital structure of the system, by computing in each case thepercentage of chaotic orbits, as well as the percentages of orbits composingthe main regular families. In an attempt to discriminate safely and withcertainty between regular and chaotic motion, we use the Smaller ALingmentIndex (SALI) method to extensive samples of orbits obtained by integratingnumerically the basic equations of motion as well as the variational equations.In addition, a technique which is based mainly on the field of spectraldynamics that utilizes the Fourier transform of the time series of eachcoordinate is used for classifying the regular orbits into different familiesand also to recognize the secondary resonances that usually bifurcate fromthem. Three cases are considered in our work: (i) the case where the ellipticalgalaxy is prolate (ii) the case where a spherically symmetric elliptical galaxyis present and (iii) the case where the elliptical galaxy has an oblate shape.Comparison between the current results and early related work is also made.

Classifying orbits in a new dynamical model describing motion in a prolate or an oblate elliptical galaxy