标题： 变分法在平面Sitnikov问题中构造同宿和异宿轨道 显示英文标题

标题： Variational Construction of Homoclinic and Heteroclinic Orbits in the Planar Sitnikov Problem

摘要： 赛特尼克夫问题是三体问题的一个特例。 该系统已知是混沌的，并且通过符号动力学进行了研究（J. Moser，稳定与随机运动在动力系统中，普林斯顿大学出版社，1973年）。 我们研究当大质量粒子的偏心率趋近于1时赛特尼克夫问题的极限情况。 通过变分法，我们在平面赛特尼克夫问题中证明了存在无限多的同宿和异宿解。 在之前的研究中，第二作者对于某些周期符号序列，证明了实现这些序列的周期解的存在性。 在本文中，我们证明了某些实现特定非周期符号序列的周期轨道之间的同宿和异宿解的存在性。 显示英文摘要

摘要： The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). We study the limiting case of the Sitnikov problem as the eccentricity of the massive particles tends to 1. By variational method, we show the existence of infinitely many homoclinic and heteroclinic solutions in the planar Sitnikov problem. In a previous work, for certain periodic symbolic sequences, the second author showed the existence of periodic solutions realizing them. In this paper, we show the existence of homoclinic and heteroclinic solutions between some of these periodic orbits which realize certain non-periodic symbolic sequences.