Orbit classification in a galaxy model with a biaxial dark matter halo

This paper presents an analysis of a galaxy model with axial symmetry that includes a spherical nucleus, a disk, and a biaxial halo composed of dark matter. The aim is to provide a complete overview of the orbital dynamics of the galactic system and determine the impact of the flattening parameter of the dark matter halo using various numerical methods. Additionally, a comprehensive presentation of the system’s network of symmetric periodic orbits is provided. The findings indicate that the flattening parameter has a reduced effect on the network of symmetric periodic orbits when an oblate halo component is considered, as compared to the case when the prolate halo is present. Finally, the study reveals that the convergence of the characteristic curves of the orbital families with multiplicities 2, 3, 4, and 5 strongly depends on the flattening parameter.