Revealing the Newton–Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem. (October 2018)

• Record Type: Journal Article
• Authors: Zotos, Euaggelos E.; Suraj, Md Sanam; Jain, Mamta; Aggarwal, Rajiv
• Is Part Of: International journal of non-linear mechanics. Volume 105(2018)
• Page Start: 43
• Page End: 54
• Publication Date: 2018-10
• Subjects: Sitnikov problem -- Pseudo-Newtonian dynamics -- Basins of convergence -- Fractal basin boundaries; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2018.07.005
• Languages: English
• ISSNs: 0020-7462

Abstract

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. Highlights: The Sitnikov problem with pseudo-Newtonian dynamics is considered. The parametric evolution of the equilibrium points is monitored. The Newton–Raphson basins of convergence on the complex plane are revealed. The basin entropy of the complex plane is calculated.