Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

Abstract

The Newton-Raphson basins of convergence, corresponding to the coplanar libration points (which act as attractors), are unveiled in the Copenhagen problem, where instead of the Newtonian potential and forces, a quasi-homogeneous potential created by two primaries is considered. The multivariate version of the Newton-Raphson iterative scheme is used to reveal the attracting domain associated with the libration points on various type of two-dimensional configuration planes. The correlations between the basins of convergence and the corresponding required number of iterations are also presented and discussed in detail. The present numerical analysis reveals that the evolution of the attracting domains in this dynamical system is very complicated, however, it is a worth studying issue.

Published in International Journal of Non-Linear Mechanics (IJNLM)

References in corpus (5)

• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
• Basins of attraction of equilibrium points in the planar circular restricted five-body problem
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem
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Cited by in corpus (6)

• The analysis of restricted five-body problem within frame of variable mass
• 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
• Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem
• On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence