Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
arXiv:1812.11849 · doi:10.1016/j.ijnonlinmec.2018.07.005
Abstract
In this paper we numerically explore the convergence properties of the pseudo-Newtonian circular restricted problem of three and four primary bodies. The classical Newton-Raphson iterative scheme is used for revealing the basins of convergence and their respective fractal basin boundaries on the complex plane. A thorough and systematic analysis is conducted in an attempt to determine the influence of the transition parameter on the convergence properties of the system. Additionally, the roots (numerical attractors) of the system and the basin entropy of the convergence diagrams are monitored as a function of the transition parameter, thus allowing us to extract useful conclusions. The probability distributions, as well as the distributions of the required number of iterations are also correlated with the corresponding basins of convergence.
Published in International Journal of Non-Linear Mechanics (IJNLM). arXiv admin note: text overlap with arXiv:1807.00693, arXiv:1806.11409
References in corpus (5)
- Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
- Comparing the fractal basins of attraction in the Hill problem with oblateness and radiation
- Newtonian and Pseudo-Newtonian Hill Problem
- Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem
- Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity