论文标题
Euler积分是三体问题中混乱的来源
Euler integral as a source of chaos in the three-body problem
论文作者
论文摘要
在本文中，我们从[20，21]中提出的问题从[22,9,9,3]中提出的一个问题（无论是某种功能称为“ Euler积分”）是沿着三体问题的轨迹，它是一种准整合。与我们以前的研究不同，在这里，我们关注“不受干扰的分隔”的区域，该区域因碰撞奇点而变得复杂。具体而言，我们将哈密顿量的自由度降低到两个自由度，在固定了一定的能量水平后，我们详细讨论了椭圆形和双曲线周期性轨道周围产生的三维相空间。在测量了Euler积分的变化强度（实际上很小）之后，我们发现混乱的存在与未扰动的分离质。后一个结果是通过仔细地使用[13，24，23]中开发的覆盖关系机械获得的。
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the Euler Integral (which are in fact small), we detect the existence of chaos closely to the unperturbed separatrix. The latter result is obtained through a careful use of the machinery of covering relations, developed in [13, 24, 23].
