论文标题
七阶广义Hénon-Heiles潜力的收敛分形盆地
Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential
论文作者
论文摘要
本文旨在调查在七阶广义Hénon-Heiles潜力中平衡点和相关的收敛盆地的点。使用著名的Newton-Raphson迭代剂，我们在数值上定位了平衡点的位置，同时还可以获得它们的线性稳定性。此外，我们演示了进入广义Hénon-Heiles电位的两个变量参数如何影响系统的收敛动力学以及盆地图的分形度。分形度是通过计算（边界）盆地熵以及不确定性维度来得出的。
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.
