Basins of convergence in the circular Sitnikov four-body problem with non-spherical primaries

Abstract

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 thorough 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.

Published in International Journal of Bifurcation and Chaos (IJBC) journal

References in corpus (5)

• Basin entropy: a new tool to analyze uncertainty in dynamical systems
• Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• Comparing the fractal basins of attraction in the Hill problem with oblateness and radiation
• Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem

Cited by in corpus (4)

• On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: the convex configuration
• On the Newton-Raphson basins of convergence associated with the libration points in the axisymmetric five-body problem: the concave configuration
• Unpredictability and basin entropy
• Fractal basins of attraction in a binary quasar model