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 and 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 pattern 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 attraction. 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.

中文翻译：

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二元类星体模型中的分形吸引力盆地

摘要 本文在圆形受限三体问题的框架内研究类星体的二元系统。振动点的参数演化和零速度曲线的几何形状是我们研究的关键方面之一。应用NR方法的多元形式来研究与振动点相连的引力盆地。使用 Newton-Raphson 方法的算法略有修改，以避免初始条件收敛过程中出现不必要的延迟。探讨了参数对吸引力盆地模式的影响以及初始条件收敛所需的迭代次数。我们进行了详尽的（数值）研究，以显示这些参数对吸引盆地中会聚区域的影响。我们用盆地熵的方法揭示了引力盆地中分形结构的存在。在几乎所有情况下，分形结构的存在在整个吸引力盆地中都存在。