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

## TL;DR

This study numerically explores the basins of convergence of libration points in an axisymmetric five-body gravitational system using the Newton-Raphson method, analyzing how configuration angles influence convergence regions and iteration distributions.

## Contribution

It provides a detailed numerical analysis of convergence basins in a five-body problem with a concave configuration, highlighting the effect of angle parameters on basin topology and convergence behavior.

## Key findings

- Libration points' positions vary with angle parameters.
- Basins of convergence are significantly affected by configuration angles.
- Probability distributions of iterations are characterized.

## 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 by \'{E}rdi and Czirj\'{a}k 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.