This letter deals with the derivation and analysis of a seventh-order generalization of the Hénon-Heiles potential. The new potential has axial and reflection symmetries, and finite escape energy with three channels of escape. Based on SALI indicator and exits basins, the dynamic behavior of the seventh-order system is investigated qualitatively in cases of bounded and unbounded movement. Moreover, a quantitative analysis is carried out through the percentage of chaotic orbits and the basin entropy, respectively. After classifying large sets of initial conditions of orbits for several values of the energy constant in both regimes, we observe that when the energy moves away from the critical value, the chaoticity of the system decreases and the basin structure becomes simpler with sharper and well defined bounds. Our results suggest that when the seventh-order contributions of the potential are taken into account, the system becomes less ergodic in comparison with the classical version of the Hénon-Heiles system.

这封信涉及对Hénon-Heiles势的七阶推广的推导和分析。新的电势具有轴向和反射对称性，以及具有三个逃逸通道的有限逃逸能量。基于SALI指示器和出口盆地，定性研究了有界和无界运动情况下七阶系统的动力学行为。此外，分别通过混沌轨道的百分比和盆地熵进行了定量分析。在两种状态下针对能量常数的几个值对大套轨道初始条件进行分类后，我们观察到，当能量远离临界值移动时，系统的混沌性降低，盆地结构变得更简单，轮廓更加清晰清晰。界限。