Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

2018/06/30 by Md Sanam Suraj, Euaggelos E. Zotos, Charanpreet Kaur +2 · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1016/j.ijnonlinmec.2018.04.012

published as IJNLM, vol. 103, 113-127 (2018) · Published in International Journal of Non-Linear Mechanics (IJNLM)

arxiv created 2018/06/30 · arxiv updated 2018/07/03

Abstract

The Newton-Raphson basins of convergence, corresponding to the coplanar libration points (which act as attractors), are unveiled in the Copenhagen problem, where instead of the Newtonian potential and forces, a quasi-homogeneous potential created by two primaries is considered. The multivariate version of the Newton-Raphson iterative scheme is used to reveal the attracting domain associated with the libration points on various type of two-dimensional configuration planes. The correlations between the basins of convergence and the corresponding required number of iterations are also presented and discussed in detail. The present numerical analysis reveals that the evolution of the attracting domains in this dynamical system is very complicated, however, it is a worth studying issue.

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• On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: the convex configuration

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