Basins of convergence of equilibrium points in the generalized Henon-Heiles system

摘要

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors of the convergence process), in the generalized Henon-Heiles system (GHH). The evolution of the position as well as of the linear stability of the equilibrium points, is determined, as a function of the value of the perturbation parameter. The attracting regions, on the configuration (x, y) plane, are revealed by using the multivariate version of the classical Newton-Raphson iterative algorithm. We perform a systematic investigation in an attempt to understand how the perturbation parameter affects the geometry as well as of the basin entropy of the attracting domains. The convergence regions are also related with the required number of iterations. (C) 2017 Elsevier Ltd. All rights reserved.