标题： 阿诺德扩散在完全三体问题中 显示英文标题

标题： Arnold Diffusion in the Full Three-Body Problem

摘要： 三体问题，即三个天体在相互引力作用下的运动问题，是经典力学中最古老的未解问题之一。 主要困难来自于存在不稳定和混沌的运动，这使得长期预测变得不可能。 在本文中，我们展示了完整的三体问题表现出一种称为阿诺德扩散的强大形式的不稳定性。 我们考虑了平面全三体问题，将其表述为开普勒问题和平面圆形限制性三体问题的摄动。 我们证明了系统表现出阿诺德扩散，这意味着能量可以在开普勒问题和限制性三体问题之间转移——这种能量转移与摄动参数无关。 我们的论点基于正确对齐窗口的拓扑方法，该方法被实现为计算机辅助证明的一部分。 我们演示了这种方法可以应用于天体的实际质量，以海王星-海卫一-小行星系统为例。 在这种情况下，我们得到了摄动参数范围和扩散时间的具体估计。 显示英文摘要

摘要： The full three-body problem, on the motion of three celestial bodies under their mutual gravitational attraction, is one of the oldest unsolved problems in classical mechanics. The main difficulty comes from the presence of unstable and chaotic motions, which make long-term prediction impossible. In this paper, we show that the full three-body problem exhibits a strong form of instability known as Arnold diffusion. We consider the planar full three-body problem, formulated as a perturbation of both the Kepler problem and the planar circular restricted three-body problem. We show that the system exhibits Arnold diffusion, in the sense that there is a transfer of energy -- of an amount independent of the perturbation parameter -- between the Kepler problem and the restricted three-body problem. Our argument is based on the topological method of correctly aligned windows, which is implemented into a computer assisted proof. We demonstrate that the approach can be applied to physically relevant masses of the bodies, choosing a Neptune-Triton-asteroid system as an example. In this case, we obtain explicit estimates for the range of the perturbation parameter and for the diffusion time.