具有三个自由度的哈密顿系统中的二维生成曲面和分割曲面

M. Katsanikas, Stephen Wiggins
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引用次数: 0

摘要

在我们之前的工作中,我们开发了两种方法,用于对具有三个或更多自由度的哈密顿系统的周期轨道分割面的构造进行推广。从周期轨道开始,我们将其扩展成一个环或圆柱体,然后成为能量面中的一个高维物体(见 [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b])。在本文中,我们提出了两种方法,在具有三个自由度的哈密顿系统中,不是通过周期轨道,而是通过二维曲面(二维几何对象)来构建分割曲面。为了说明这种构造算法,我们提供了三自由度哈密顿系统的基准示例。具体来说,我们采用了具有三个自由度的哈密顿系统的二次法线形式的非耦合和耦合情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
2D Generating Surfaces and Dividing Surfaces in Hamiltonian Systems with Three Degrees of Freedom
In our previous work, we developed two methods for generalizing the construction of a periodic orbit dividing surface for a Hamiltonian system with three or more degrees of freedom. Starting with a periodic orbit, we extend it to form a torus or cylinder, which then becomes a higher-dimensional object within the energy surface (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b]). In this paper, we present two methods to construct dividing surfaces not from periodic orbits but by using 2D surfaces (2D geometrical objects) in a Hamiltonian system with three degrees of freedom. To illustrate the algorithm for this construction, we provide benchmark examples of three-degree-of-freedom Hamiltonian systems. Specifically, we employ the uncoupled and coupled cases of the quadratic normal form of a Hamiltonian system with three degrees of freedom.
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