  We investigate the regular or chaotic nature of orbits of stars moving in the
meridional plane (R,z) of an axially symmetric galactic model with a dense,
massive spherical nucleus and a dark matter halo component. In particular, we
study the influence of the fractional portion of the dark matter, by computing
in each case the percentage of chaotic orbits, as well as the percentages of
orbits of the main regular resonant families. In an attempt to distinguish
between regular and chaotic motion, we use the Fast Lyapunov Indicator (FLI)
method to extensive samples of orbits obtained by integrating numerically the
equations of motion as well as the variational equations. Furthermore, a
technique which is based mainly on the field of spectral dynamics that utilizes
the Fourier transform of the time series of each coordinate is used for
identifying the various families of regular orbits and also to recognize the
secondary resonances that bifurcate from them. Two cases are studied in our
work: (i) the case where we have a disk galaxy model (ii) the case where our
model represents an elliptical galaxy. Comparison with early related work is
also made.
