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An axially symmetric galactic gravitational model composed of a dense,massive and spherical nucleus with an additional dark matter halo component wasused, to distinguish between the regular and chaotic character of orbits ofstars that move in the meridional plane (R,z). We investigated two differentcases: (i) a flat-disk galaxy (ii) an elliptical galaxy. It is of particularinterest to reveal how the portion of the dark matter inside the main body ofthe galaxy influences the ordered or chaotic nature of motion. Varying theratio of dark matter to stellar mass, we monitored the evolution not only ofthe percentage of chaotic orbits, but also of the percentages of orbits thatcompose the main regular resonant families, by classifying regular orbits intodifferent families. Moreover we tried, to reveal how the starting position ofthe parent periodic orbits of each regular family changes with respect to thefractional portion of dark matter. We compared our results with previoussimilar work.

Revealing the influence of dark matter on the nature of motion and the families of orbits in axisymmetric galaxy models