Investigating the basins of convergence in the circular Sitnikov three-body problem with non-spherical primaries

Abstract

In this work we numerically explore the Newton-Raphson basins of convergence, related to the equilibrium points, in the Sitnikov three-body problem with non-spherical primaries. The evolution of the position of the roots is determined, as a function of the value of the oblateness coefficient. The attracting regions, on several types of two dimensional planes, are revealed by using the classical Newton-Raphson iterative method. We perform a systematic and thorough investigation in an attempt to understand how the oblateness coefficient affects the geometry as well as the overall properties of the convergence regions. The basins of convergence are also related with the required number of iterations and also with the corresponding probability distributions.

Published in Few-Body Systems (FBSY) journal. arXiv admin note: substantial text overlap with arXiv:1806.11409; text overlap with arXiv:1801.01378, arXiv:1801.00710, arXiv:1803.07398, arXiv:1702.07279

References in corpus (3)

• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
• Basins of attraction of equilibrium points in the planar circular restricted five-body problem
• Slow-roll inflation from massive vector fields non-minimally coupled to gravity

Cited by in corpus (4)

• On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: the convex configuration
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
• On the convergence dynamics of the Sitnikov problem with non-spherical primaries