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

TL;DR

This study explores the complex fractal structures of convergence basins around libration points in a modified Copenhagen problem using a quasi-homogeneous Manev-type potential, revealing intricate dynamical behaviors.

Contribution

It introduces a detailed numerical analysis of Newton-Raphson basins of convergence in a non-Newtonian potential setting for the Copenhagen problem, highlighting new fractal basin structures.

Findings

Basins of convergence exhibit complex fractal boundaries.

The evolution of attracting domains is highly intricate.

Correlation between basins and iteration counts is analyzed.

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.