Comparing the fractal basins of attraction in the Hill problem with oblateness and radiation

TL;DR

This study explores the complex fractal basins of attraction in the Hill problem considering oblateness and radiation, revealing intricate patterns and their dependence on system parameters through extensive numerical analysis.

Contribution

It provides a detailed numerical investigation of the fractal basins of attraction in the Hill problem with oblateness and radiation, highlighting their structure and dependence on parameters.

Findings

Basins of convergence exhibit highly fractal and beautiful formations.

The structure of basins depends on oblateness and radiation parameters.

Number of iterations correlates with basin boundaries complexity.

Abstract

The basins of convergence, associated with the roots (attractors) of a complex equation, are revealed in the Hill problem with oblateness and radiation, using a large variety of numerical methods. Three cases are investigated, regarding the values of the oblateness and radiation. In all cases, a systematic and thorough scan of the complex plane is performed in order to determine the basins of attraction of the several iterative schemes. The correlations between the attracting domains and the corresponding required number of iterations are also illustrated and discussed. Our numerical analysis strongly suggests that the basins of convergence, with the highly fractal basin boundaries, produce extraordinary and beautiful formations on the complex plane.