Revealing the basins of convergence in the planar equilateral restricted four-body problem

Abstract

The planar equilateral restricted four-body problem where two of the primaries have equal masses is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position of the libration points is monitored when the value of the mass parameter $m_3$ varies in predefined intervals. The regions on the configuration $(x,y)$ plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson iterative scheme. The correlations between the attracting domains of the equilibrium points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We perform a thorough and systematic numerical investigation by demonstrating how the dynamical parameter $m_3$ influences the shape, the geometry and the degree of fractality of the converging regions. Our numerical outcomes strongly indicate that the mass parameter is indeed one of the most influential factors in this dynamical system.

Published in Astrophysics and Space Science (A&SS) journal

References in corpus (2)

• In the Shadow of the Transiting Disk: Imaging epsilon Aurigae in Eclipse
• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

Cited by in corpus (7)

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• 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
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem