On the basins of convergence in the magnetic-binary problem with angular velocity

Abstract

The restricted three-body problem, where the primaries are magnetic dipoles, is discussed. In the predefined interval, the effect of the varying values of mass parameter $\mu$ and the angular velocity $\omega$ on the parametric variation of locations of the equilibrium points are illustrated. Indeed, the influence of the values of the ratio $\lambda$ of the magnetic moments in the presence of angular velocity $\omega$ on the topology of the basins of convergence is discussed. The bivariate version of the well-known Newton–Raphson scheme is used to illustrate the basins of convergence on the configuration (x, y) plane. In addition, the correlations betwixt the basins of convergence associated to the equilibrium points and the linked number of iterations required to assure the preassumed precision are discussed. In this study, a rigorous and structured numerical investigation are illustrated by exhibiting how the values of $\lambda$ and $\omega$ have significant influence on the shape, the topology and also the degree of fractality of the domain of basins of convergence. The results and outcomes of present study strongly indicate that the parameters $\omega ,\mu$, and $\lambda$ have significant influence in the electromagnetic binary system.