论文标题
关于七阶广义的Hénon-Heiles潜力的动力学
On the dynamics of a seventh-order generalized Hénon-Heiles potential
论文作者
论文摘要
本文介绍了Hénon-Heiles潜力的七阶概括的推导和分析。新电势具有轴向和反射对称性，并具有三个逃生通道的有限逃逸能量。基于SALI指标和退出盆地，在有界和无界运动的情况下，对七阶系统的动态行为进行了定性研究。此外，分别通过混沌轨道和盆地熵的百分比进行了定量分析。在将大量的轨道的初始条件分类为两个方案中能量常数的几个值的初始条件之后，我们观察到，当能量从临界值移开时，系统的混沌性会降低，而盆地结构随着更加敏锐和定义明确的边界而变得更加简单。我们的结果表明，当考虑到电势的七阶贡献时，与Hénon-Heiles系统的经典版本相比，系统变得不那么奇妙。
This paper 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.
