Unpredictable basin boundaries in restricted six-body problem with square configuration (2005.04893v1)

Abstract: 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.