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

2018/06/29 by Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal +1 · 2 citations
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1007/s00601-018-1393-8

published as FBSY, vol. 58:69 (2018) · 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

arxiv created 2018/06/29 · arxiv updated 2018/07/03

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.

Citations

• Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries
• Basins of attraction of equilibrium points in the planar circular restricted five-body problem
• Basins of convergence of equilibrium points in the generalized Hill problem
• Basins of convergence of equilibrium points in the generalized Henon-Heiles system
• Revealing the basins of convergence in the planar equilateral restricted four-body problem

Cited by

• On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate primaries
• Revealing the Newton–Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem

Related

• Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries
• Basins of attraction of equilibrium points in the planar circular restricted five-body problem
• Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential
• Basins of convergence of equilibrium points in the generalized Henon-Heiles system
• A generalized Sitnikov problem