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

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.

arXiv commentPublished in Astrophysics and Space Science (A&SS) journal

References in corpus (4)

• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
• Stability Regions of Equilibrium Points in Restricted Four-Body Problem with Oblateness Effects
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• Determining the Newton-Raphson basins of attraction in the electromagnetic Copenhagen problem

Cited by in corpus (10)

• Basins of attraction of equilibrium points in the planar circular restricted five-body problem
• On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate primaries
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• Basins of convergence in the circular Sitnikov four-body problem with non-spherical primaries
• Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
• Comparing the geometry of the basins of attraction, the speed and the efficiency of several numerical methods
• Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries
• The perturbed restricted three-body problem with angular velocity: Analysis of basins of convergence linked to the libration points
• On the convergence dynamics of the Sitnikov problem with non-spherical primaries