论文标题
二进制类星体模型中吸引力的分形盆地
Fractal basins of attraction in a binary quasar model
论文作者
论文摘要
本文在循环限制的三体问题的框架内研究了类星体的二元系统。文库点的参数演化，零速度曲线的几何形状是我们研究的关键方面之一。 NR方法的多元形式用于研究与库点相关的吸引力盆地。为了避免初始条件收敛的不必要延迟，用于使用牛顿 - 拉夫森方法的算法进行了稍微修改。参数对吸引盆地形状的影响以及初始条件收敛所需的迭代次数。我们进行了一项详尽的（数值）研究，以显示这些参数对收敛盆地收敛区域的影响。我们使用盆地熵方法推出了吸引盆地中分形结构的存在。在几乎所有情况下，在吸引力的整个盆地中都存在分形结构的存在。
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.
