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.

On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: The convex configuration

“…Recently, the above mentioned iterative scheme has been used to unveil the basins of convergence in various types of dynamical systems, such as the restricted fivebody problem (e.g., [18]), the restricted four-body problem ( [19,20], [21,22]), the Sitnikov problem (e.g., [23,24]), the collinear four-body problem, in the Copenhagen case with a repulsive quasi-homogeneous Manev-type potential (e.g., [25]), the out-of-plane libration points in the case of the few-body problem (e.g., [26], [27]) and of course the restricted three-body problem (e.g., [28,29]).…”

On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence

“…In the past few years, the Newton-Raphson basins of convergence have been studied by many authors in various dynamical system, i.e., the restricted three-body problem (e.g., [29], [33], [34]), the restricted four-body problem (e.g., [26,27,28,30]), the axisymmetric restricted five-body problem (e.g., [22,23]), restricted five-body problem (e.g., [24], [32]). The basins of convergence, linked with the libration points of the dynamical system, provide some of the most intrinsic properties of these systems.…”

Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem

“…The existence of equilibrium points in the restricted problem of three bodies (e.g., [22]), their stability (e.g., [1]), the existence of periodic orbits around the equilibrium points (e.g., [2]), the stability of the libration points in linear and non-linear sense with heterogeneous primaries (e.g., [31], [29]), the restricted three-body problem by taking smaller primary as an ellipsoid (e.g., [21]), and the basins of convergence associated with the libration points in the photogravitational restricted problem of three bodies (e.g., [39]) are some characteristic examples. The effect of the oblateness of the primaries (e.g., [28]), the radiation due to the primaries (e.g., [10]) and the effect of small perturbations in the Coriolis and centrifugal forces (e.g., [9,11]), the copenhagen problem with repulsive Manev potential (e.g., [36]) are the most important perturbations that have been considered.…”