2018/07/18 by Euaggelos E. Zotos, Md Sanam Suraj, Mamta Jain +1
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Attractor #Convergence (economics) #Fractal #Geology #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Newton's method #Nonlinear system #Physics #Structural basin #Theoretical and Computational Physics #Tribology and Lubrication Engineering #nlin.CD
paper · pdf · doi:10.1016/j.ijnonlinmec.2018.07.005
published as IJNLM, vol. 105, 43-54 (2018) · Published in International Journal of Non-Linear Mechanics (IJNLM). arXiv admin note: text overlap with arXiv:1807.00693, arXiv:1806.11409
openalex publication_date 2018/07/18 · openalex created_date 2018/08/03 · arxiv created 2018/12/27 · arxiv updated 2019/01/01 · openalex updated_date 2026/08/05
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.