On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration

Abstract

The axisymmetric five-body problem with the concave configuration has been studied numerically to reveal the basins of convergence, by exploring the Newton-Raphson iterative scheme, corresponding to the coplanar libration points (which act as attractors). In addition, four primaries are set in axisymmetric central configurations introduced byÉrdi and Czirják [13] and the motion is governed by mutual gravitational attraction only. The evolution of the positions of libration points is illustrated, as a function of the value of angle parameters. A systematic and rigorous investigation is performed in an effort to unveil how the angle parameters affect the topology of the basins of convergence. In addition, the relation of the domain of basins of convergence with required number of iterations and the corresponding probability distributions are illustrated.

On the axisymmetric restricted five-body problem within the frame of variable mass: The convex case

“…There are various applications of the restricted five-body problem, in celestial mechanics, dynamical astronomy, and galactic dynamics, which have been pre-owned by some researchers like Ollöngren (1988), Papadakis and Kanavos (2007) etc. There are many scientists and researchers who worked on the restricted five-body problem, among them few are as follows: Gao et al (2017), Suraj et al (2019b), Suraj et al (2019c), Suraj et al (2019d) and Suraj et al (2019e) along with the references therein.…”

The study of the fractal basins of convergence linked with equilibrium points in the perturbed (N+ 1)‐body ring problem

“…In the past few years, many authors have discussed the topology of the BoC linked to the equilibrium points of the system using a bivariate version of the NR method in various dynamical systems, especially in the perturbed restricted problem of three, four, and five bodies. Some of them are: the axisymmetric restricted five‐body problem (Suraj et al 2019a, 2019b, 2019c), restricted five‐body problem (R5BP) with variable mass (Suraj et al 2019d), the R4BP (Suraj et al 2017a, 2017b, 2018a, 2018c), and the Copenhagen problem (Suraj et al 2018b; Zotos 2018).…”

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

“…[22], in the concave case, see Ref. [23], the five-body problem when the mass of the test particle is variable, see Ref. [24] and the effect of Coriolis and centrifugal force in the axisymmetric five-body problem, see Ref.…”

“…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.…”