Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity

Abstract

The planar linear restricted four-body problem is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position as well as of the stability of the libration points is monitored when the values of the mass parameter $b$ as well as of the angular velocity $\omega$ vary 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 parameters $b$ and $\omega$ influence the shape, the geometry and of course the fractality of the converging regions. Our numerical outcomes strongly indicate that these two parameters are indeed two of the most influential factors in this dynamical system.

Published in Chaos, Solitons and Fractals journal (CSF). arXiv admin note: previous papers with related context: arXiv:1702.07279, arXiv:1704.02273

References in corpus (1)

• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

Cited by in corpus (5)

• 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
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem