AI 中文总结
该研究通过 Levi-Civita 正则化等方法，证明地月平面圆限制性三体问题中存在趋向碰撞与无穷远的振荡运动，且各类运动可结合、存在任意大的 ejection/collision 轨道，为相关问题提供计算机辅助的严格证明。
AI 中文摘要
我们给出了地月平面圆限制性三体问题中趋向碰撞与无穷远的振荡运动存在性的计算机辅助证明。特别地，我们证明所有类型的运动（双曲型、抛物型、趋向无穷远的振荡型、趋向碰撞的振荡型及终止于碰撞的运动）均可结合，还证明了存在任意大的 ejection/collision 轨道。该结果通过 Levi-Civita 正则化、McGehee 正则化、拓扑工具及严格数值计算实现。
英文摘要
We present a computer assisted proof of the existence of the oscillatory motion to collision and to infinity in the Earth-Moon planar circular restricted three body problem. In particular, we show that all types of motion (hyperbolic, parabolic, oscillatory to infinity, oscillatory to collision and terminating in collision) can be combined. We also prove the existence of arbitrarily large ejection/collision orbits. The results are achieved with the use of the Levi-Civita regularization, the McGehee regularization, topological tools and rigorous numerical computations.
Comments41 pages, 8 figures
