The aim of our work is to numerically explore the equilibrium points and the respective basins of convergence in the case of the circular restricted problem, where the two primaries are prolate. The coordinates of the libration points are derived by deploying the Newton–Raphson root method, while we also investigated the linear stability of the equilibrium points. Moreover, we also demonstrate the influence of the parameters controlling the prolateness of the primaries on the convergence dynamics of the problem. The degree of fractality of the basin diagrams on the configuration plane is estimated by calculating both the uncertainty dimension and the (boundary) basin entropy.

中文翻译：

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受限原形约束三体问题中均衡的收敛性

我们的工作目的是在圆形初等问题为圆形的受限问题的情况下，以数值方式探索平衡点和收敛的各个盆地。释放点的坐标是通过部署牛顿-拉夫森根法得出的，同时我们还研究了平衡点的线性稳定性。此外，我们还证明了控制原色分布的参数对问题收敛动力学的影响。通过计算不确定性维数和（边界）盆地熵，可以估算出配置图上盆地图的分形程度。