# On the convergence dynamics of the Sitnikov problem with non-spherical primaries

## TL;DR

This study explores how the shape of celestial bodies affects the convergence behavior of the Newton-Raphson method in the Sitnikov problem, revealing the influence of oblateness on convergence speed, efficiency, and basin fractality.

## Contribution

It provides a detailed numerical analysis of the impact of oblateness on convergence dynamics and basin fractality in the Sitnikov problem, which was not previously examined.

## Key findings

- Oblateness parameter A significantly affects convergence speed.
- Convergence basins exhibit fractal structures influenced by oblateness.
- Higher oblateness increases basin boundary complexity.

## Abstract

We investigate, using numerical methods, the convergence dynamics of the Sitnikov problem with non-spherical primaries, by applying the Newton-Raphson (NR) iterative scheme. In particular, we examine how the oblateness parameter $A$ influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the convergence basins on the plane of complex numbers. Moreover, we compute the degree of fractality of the convergence basins on the complex space, as a relation of the oblateness, by using different computational tools, such the fractal dimension as well as the (boundary) basin entropy.