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Basins of attraction of equilibrium points in the planar circular restricted five-body problem

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Abstract

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability of the equilibrium points is determined, as a function of the value of the mass parameter. The attracting regions, on several types of two dimensional planes, are revealed by using the multivariate version of the classical Newton-Raphson iterative method. We perform a systematic investigation in an attempt to understand how the mass parameter affects the geometry as well as the degree of fractality of the basins of attraction. The regions of convergence are also related with the required number of iterations and also with the corresponding probability distributions.

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Notes

  1. By the term fractal we simply mean that the particular area has a fractal-like geometry, without conducting any additional calculations, until for now, as in Aguirre et al. (2001).

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Acknowledgements

The authors would like to express their warmest thanks to the anonymous referees for the careful reading of the manuscript and for all the apt suggestions and comments which allowed us to improve both the quality and the clarity of the paper.

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Authors and Affiliations

  1. Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece

    Euaggelos E. Zotos

  2. Department of Mathematics, SGTB Khalsa College, University of Delhi, North Campus, New Delhi, 110007, India

    Md Sanam Suraj

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  1. Euaggelos E. Zotos
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  2. Md Sanam Suraj
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Correspondence to Euaggelos E. Zotos.

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Zotos, E.E., Sanam Suraj, M. Basins of attraction of equilibrium points in the planar circular restricted five-body problem. Astrophys Space Sci 363, 20 (2018). https://doi.org/10.1007/s10509-017-3240-7

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