The perturbed restricted three-body problem with angular velocity: Analysis of basins of convergence linked to the libration points

TL;DR

This paper investigates how angular velocity affects the structure of convergence basins around libration points in a radiating restricted three-body system, using Newton-Raphson method and basin entropy analysis.

Contribution

It introduces a detailed analysis of the impact of angular velocity on convergence basins and their fractality in the perturbed restricted three-body problem with radiation.

Findings

Angular velocity significantly alters the topology of convergence basins.

The fractality of the basins varies with system parameters, quantified by basin entropy.

The Newton-Raphson method effectively maps the convergence regions around libration points.

Abstract

The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate scheme of the Newton-Raphson (N-R) iterative method has been used to discuss the topology of the basins of convergence. The parametric evolution of the fractality of the convergence plane is also presented where the degree of fractality is illustrated by evaluating the basin entropy of the convergence plane.