On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate primaries
arXiv:1807.00877 · doi:10.1016/j.ijnonlinmec.2018.05.002
Abstract
The Copenhagen case of the circular restricted three-body problem with oblate primary bodies is numerically investigated by exploring the Newton-Raphson basins of convergence, related to the out-of-plane equilibrium points. The evolution of the position of the libration points is determined, as a function of the value of the oblateness coefficient. The attracting regions, on several types of two-dimensional planes, are revealed by using the multivariate Newton-Raphson iterative method. We perform a systematic and thorough investigation in an attempt to understand how the oblateness coefficient affects the geometry of the basins of convergence. The convergence regions are also related with the required number of iterations and also with the corresponding probability distributions. The degree of the fractality is also determined by calculating the fractal dimension and the basin entropy of the convergence planes.
Published in International Journal of Non-Linear Mechanics (IJNLM). arXiv admin note: text overlap with arXiv:1801.01378, arXiv:1806.11409, arXiv:1807.00693
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
- Basins of attraction of equilibrium points in the planar circular restricted five-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 (6)
- The analysis of restricted five-body problem within frame of variable mass
- 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
- A test for fractal boundaries based on the basin entropy
- Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
- On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence