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Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem

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Abstract

The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation of the position as well as of the stability of the equilibrium points is determined, when the value of the transition parameter \(\epsilon \) varies in the interval \([0,1]\). The multivariate Newton-Raphson iterative scheme is used to determine the attracting domains on several types of two-dimensional planes. A systematic and thorough numerical investigation is performed in order to demonstrate the influence of the transition parameter on the geometry of the basins of convergence. The correlations between the basins of attraction and the corresponding required number of iterations are also illustrated and discussed. Our numerical analysis strongly indicates that the evolution of the attracting regions in this dynamical system is an extremely complicated yet very interesting issue.

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Notes

  1. When it is stated that a region is fractal we simply mean that it has a fractal-like geometry, without conducting any additional calculations for computing the fractal dimension as in Aguirre et al. (2001).

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

    Euaggelos E. Zotos

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Zotos, E.E. Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem. Astrophys Space Sci 362, 195 (2017). https://doi.org/10.1007/s10509-017-3172-2

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