Basins of convergence of equilibrium points in the generalized Hill problem

Abstract

The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the generalized Hill problem. The parametric variation of the position and the linear stability of the equilibrium points is determined, when the value of the perturbation parameter $\epsilon$ varies. The multivariate Newton-Raphson iterative scheme is used to determine the attracting domains on several types of two-dimensional planes. A systematic and thorough numerical investigation is performed in order to demonstrate the influence of the perturbation parameter on the geometry as well as of the basin entropy of the basins of convergence. The correlations between the basins of attraction and the corresponding required number of iterations are also illustrated and discussed. Our numerical analysis strongly indicates that the evolution of the attracting regions in this dynamical system is an extremely complicated yet very interesting issue.

Published in International Journal of Bifurcation and Chaos (IJBC) journal. This paper belongs to a series of papers (e.g., arXiv:1710.03598, arXiv:1702.07279) in which we numerically investigate the Newton-Raphson basins of convergence in several types of Hamiltonian systems

References in corpus (4)

• 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
• Determining the Newton-Raphson basins of attraction in the electromagnetic Copenhagen problem

Cited by in corpus (1)

• Equilibrium points and basins of convergence in the triangular restricted four-body problem with a radiating body