Unpredictable basin boundaries in restricted six-body problem with square configuration |
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| Institution: | 1. Department of Mathematics, Zakir Husain Delhi College, University of Delhi, Delhi 110002, India;2. Department of Mathematics, College of Natural and Computational Science, Mizan-Tepi University, Tepi Campus, Ethiopia;1. Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran;2. Young Researchers and Elite Club, Science and Research Branch, Islamic Azad University, Tehran, Iran;3. Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran, Iran |
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| Abstract: | The present work deals with the recently introduced restricted six body-problem with square configuration. We have computed and verified the position of libration points with the help of Newton-Raphson method. It is observed that the total number of libration points are either twelve or twenty depends upon the mass parameter μ ∈ (0, 0.25). The multivariate form of Newton-Raphson scheme is used to discuss the basins of attraction. Different aspects of the basins 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 μ ∈ (0.215, 0.238), the basins of attraction are unpredictable throughout. It is observed that for all values of the mass parameter μ, the basin boundaries are highly unpredictable. Moreover, we have investigated the presence of Wada basin boundary in the basin of attraction. |
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