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

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.

Published in Astrophysics and Space Science (A&SS) journal. Previous paper with related context: arXiv:1801.00710

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• Revealing the basins of convergence in the planar equilateral restricted four-body problem
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Cited by in corpus (12)

• The analysis of restricted five-body problem within frame of variable mass
• On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate primaries
• On the spatial collinear restricted four-body problem with non-spherical primaries
• On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: the convex configuration
• Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• A test for fractal boundaries based on the basin entropy
• Investigating the basins of convergence in the circular Sitnikov three-body problem with non-spherical primaries
• Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem
• Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries
• The perturbed restricted three-body problem with angular velocity: Analysis of basins of convergence linked to the libration points
• Classifying basins of attraction using the basin entropy