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

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.

arXiv commentPublished in Astrophysics and Space Science (A&SS) journal. Previous papers with related context: arXiv:1702.07279, arXiv:1706.07044, arXiv:1704.02273, arXiv:1709.06631

References in corpus (6)

• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
• Stability Regions of Equilibrium Points in Restricted Four-Body Problem with Oblateness Effects
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• Pseudo-Newtonian planar circular restricted 3-body problem
• On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem
• Determining the Newton-Raphson basins of attraction in the electromagnetic Copenhagen problem

Cited by in corpus (10)

• On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate 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
• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Basins of convergence of equilibrium points in the generalized Henon-Heiles system
• Basins of convergence in the circular Sitnikov four-body problem with non-spherical primaries
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
• Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem
• Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries
• Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential