Fractal basins of attraction in a binary quasar model

Abstract

The present paper investigates the binary system of quasars in the framework of the Circular Restricted Three-Body Problem. The parametric evolution of libration points, the geometry of zero-velocity curves are one of the crucial aspects of our study. The multivariate form of NR method is applied to study the basin of attraction connected with libration points. The algorithm for using the Newton-Raphson method is slightly modified in order to avoid the unnecessary delay in the convergence of initial conditions. The impact of parameters on the shape of the basin of attraction and the number of iterations needed for the convergence of initial conditions are explored. We carry out an exhaustive (numerical) study to show the influence of these parameters on converging regions in basins of convergence. We unveil the existence of fractal structure in the basin of attraction using the method of basin entropy. In almost all cases, the existence of fractal structure is found throughout the basins of attraction.

arXiv comment16 pages, 8 figures

References in corpus (8)

• Basin entropy: a new tool to analyze uncertainty in dynamical systems
• On-axis spectroscopy of the host galaxies of 20 optically luminous quasars at z~0.3
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• Chaotic dynamics and fractal structures in experiments with cold atoms
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• Basins of convergence in the circular Sitnikov four-body problem with non-spherical primaries
• Order and Chaos in a Three-dimensional Binary System of Interacting Galaxies
• Unpredictable basin boundaries in restricted six-body problem with square configuration