Spinning compact object and chaos in galactic centers
Galactic centres are highly dynamic regions dominated by a supermassive black hole (BH) surrounded by nuclear star clusters (NSC), molecular gas, and asymmetric matter distributions such as disks or halos. The combined gravitational effects of these components, along with relativistic corrections from the BH's spin, generate strongly nonlinear dynamics and frequent chaotic orbital behaviour. To model this environment, we employ a multipolar expansion potential in which the central compact object is represented by the Artemova-Bjornsson-Novikov pseudo-Newtonian potential, effectively capturing spin-dependent features of a Kerr-like BH. The surrounding halo is treated as an axisymmetric, shell-like mass distribution expanded up to third order in multipolar terms to account for realistic asymmetry. Previous studies have mainly explored the influence of multipolar moments and BH spin using Poincare sections, SALI, and related chaos indicators. In this work, we extend these analyses by incorporating stability analysis and basins of convergence to achieve a more complete understanding of the system's dynamics. Stability analysis around equilibrium points provides insight into local behavior, while basins of convergence highlight sensitivity to initial conditions and expose fractal basin boundaries. Our results show that the BH spin significantly reshapes phase space: depending on its magnitude and orientation, it can either amplify chaotic scattering caused by halo asymmetry or stabilize specific orbital families. These findings enhance our understanding of how relativistic spin effects and multipolar mass distributions jointly govern the dynamical architecture of galactic centers.