Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries

Euaggelos E. Zotos, Satyendra Kumar Satya, Rajiv Aggarwal, Sanam Suraj
2018 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
The Newton-Raphson basins of convergence, related to the equilibrium points, in the Sitnikov four-body problem with non-spherical primaries are numerically investigated. We monitor the parametric evolution of the positions of the roots, as a function of the oblateness coefficient. The classical Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and
more » ... ough analysis in an attempt to understand how the oblateness coefficient affects the geometry as well as the basin entropy of the convergence regions. The convergence areas are related with the required number of iterations and also with the corresponding probability distributions.
doi:10.1142/s0218127418300161 fatcat:dgfvhqkmyjhzjb73ivd3pdojmq