三自由度哈密顿系统周期轨道划分曲面的推广-ⅲ

M. Katsanikas, S. Wiggins
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引用次数: 0

摘要

在之前的两篇论文[Katsanikas & Wiggins, 2021a, 2021b]中,我们开发了两种方法来构建具有三个或更多自由度的哈米顿系统的周期轨道分度面。我们将第一种方法(参见[Katsanikas & Wiggins, 2021a])应用于具有三自由度的范式二次哈密顿系统,在5D能量面中构造一个几何对象,该几何对象是四维环面结构的截面,其空间为[公式:见文本]。我们提供了一个更详细的几何描述这个对象的家庭内的四维地形。我们证明了这个物体是一个分面,并且它具有不相交的性质。在本文中,我们将结果推广到全四维环面物体在五维能量面上的情况。然后在三自由度耦合二次范式哈密顿系统的5D能量面上计算该环面物体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom-III
In two previous papers [Katsanikas & Wiggins, 2021a, 2021b], we developed two methods for the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom. We applied the first method (see [Katsanikas & Wiggins, 2021a]) in the case of a quadratic Hamiltonian system in normal form with three degrees of freedom, constructing a geometrical object that is the section of a 4D toroidal structure in the 5D energy surface with the space [Formula: see text]. We provide a more detailed geometrical description of this object within the family of 4D toratopes. We proved that this object is a dividing surface and it has the no-recrossing property. In this paper, we extend the results for the case of the full 4D toroidal object in the 5D energy surface. Then we compute this toroidal object in the 5D energy surface of a coupled quadratic normal form Hamiltonian system with three degrees of freedom.
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