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

Abstract

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 Hénon-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.

Published in International Journal of Non-Linear Mechanics (IJNLM). Previous papers with related context: arXiv:1801.01378

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
• Chaotic dynamics and fractal structures in experiments with cold atoms
• Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem
• Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system

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