Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential

Abstract

This article aims to investigate the points of equilibrium and the associated convergence basins in a seventh-order generalized Hénon-Heiles potential. Using the well-known Newton-Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, we demonstrate how the two variable parameters, entering the generalized Hénon-Heiles potential, affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy as well as the uncertainty dimension.

11 pages, 8 figures

References in corpus (4)

• 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
• On the dynamics of a seventh-order generalized Hénon-Heiles potential