2018/01/02 by Euaggelos E. Zotos · 2 citations
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1142/s0218127417300439
published as IJBC, Vol. 27, No. 12 (2017) 1730043 (18 pages) · 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
arxiv created 2018/01/02 · arxiv updated 2018/03/28
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 ε 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.