Revealing the influence of dark matter on the nature of motion and the
  families of orbits in axisymmetric galaxy models
  An axially symmetric galactic gravitational model composed of a dense,
massive and spherical nucleus with an additional dark matter halo component was
used, to distinguish between the regular and chaotic character of orbits of
stars that move in the meridional plane (R,z). We investigated two different
cases: (i) a flat-disk galaxy (ii) an elliptical galaxy. It is of particular
interest to reveal how the portion of the dark matter inside the main body of
the galaxy influences the ordered or chaotic nature of motion. Varying the
ratio of dark matter to stellar mass, we monitored the evolution not only of
the percentage of chaotic orbits, but also of the percentages of orbits that
compose the main regular resonant families, by classifying regular orbits into
different families. Moreover we tried, to reveal how the starting position of
the parent periodic orbits of each regular family changes with respect to the
fractional portion of dark matter. We compared our results with previous
similar work.
