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The unpredictability of the basins of attraction in photogravitational Chermnykh’s problem
Astrophysics and Space Science ( IF 1.9 ) Pub Date : 2020-06-01 , DOI: 10.1007/s10509-020-03815-4
Vinay Kumar , Pankaj Sharma , Rajiv Aggarwal , Sushil Yadav , Bhavneet Kaur

This paper deals with the photogravitational circular restricted three-body problem, including the effect of circular cluster of material points. The parametric evolution of the position of equilibrium points and the existence of a different number of equilibrium points are illustrated using graphs. A detailed investigation to find out the influence of the radiation pressure q $q$ , mass ratio μ $\mu $ and the circular cluster of material points M b $M_{b}$ on the geometry of basins of attraction is carried out. Further, the number of iterations required to obtain the desired level of accuracy is recorded and presented using probability distribution diagram. The correlations between the domain of convergence of equilibrium points and the corresponding number of the iterations required to obtain the desired level of accuracy are explained. We monitor the parametric evolution of the basin entropy to reveal the unpredictability in the basins of attractions. It is found that unpredictable (fractal) regions exist in the vicinity of boundaries of the basins of attraction.

中文翻译:

光引力 Chermnykh 问题中引力盆地的不可预测性

本文处理光引力圆形受限三体问题,包括物质点圆形簇的影响。平衡点位置的参数演化和不同数量的平衡点的存在用图表说明。详细研究了辐射压力 q $q$ 、质量比 μ $\mu $ 和物质点的圆形簇 M b $M_{b}$ 对吸引盆几何形状的影响。此外,使用概率分布图记录和呈现获得所需精度水平所需的迭代次数。解释了平衡点的收敛域与获得所需精度水平所需的相应迭代次数之间的相关性。我们监测盆地熵的参数演化,以揭示景点盆地的不可预测性。发现在吸引力盆地的边界附近存在不可预测的(分形)区域。
更新日期:2020-06-01
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