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Unpredictable basin boundaries in restricted six-body problem with square configuration
New Astronomy ( IF 2 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.newast.2020.101451
Vinay Kumar , M. Javed Idrisi , M. Shahbaz Ullah

The present work deals with the recently introduced restricted six body-problem with square configuration. It is determined that the total number of libration points are twelve and twenty for the mass parameter $0< \mu < 0.25$. The multivariate form of Newton-Raphson scheme is used to discuss the basin of attraction. Different aspects of the basin of attraction are investigated and explained in detail. The complex combination of the different basins is found along the boundaries. The concept of basin entropy is used to unveil the nature of the boundaries. For $\mu = 0.22$ and $0.23$, the basin of attraction is unpredictable throughout. It is observed that for all values of the mass parameter $\mu$, the basin boundaries are highly unpredictable. Further, We have investigated the presence of Wada basin boundary in the basin of attraction.

中文翻译:

方形构型受限六体问题中不可预测的盆地边界

目前的工作处理最近引入的具有方形配置的受限六体问题。对于质量参数$0<\mu<0.25$,确定振动点的总数为十二和二十。Newton-Raphson 方案的多元形式用于讨论吸引力盆地。对吸引力盆地的不同方面进行了详细的调查和解释。沿边界发现了不同盆地的复杂组合。盆地熵的概念用于揭示边界的性质。对于 $\mu = 0.22$ 和 $0.23$,吸引力盆地始终是不可预测的。据观察,对于质量参数 $\mu$ 的所有值,盆地边界是高度不可预测的。此外,我们还调查了吸引力盆地中和田盆地边界的存在。
更新日期:2021-01-01
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