Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential

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