行星三体问题中极大环面与须状环面的共存
动力系统
2018-09-21 v4
摘要
本文讨论了在三体问题相空间区域中稳定与不稳定拟周期 KAM 环面“共存”的可能性。证明的思路沿循 KAM 理论，特别是，在同一相空间区域中构造两个非光滑相关的正则坐标系；对于“适当退化”系统，Nekhorossev 与 Miščenko 和 Fomenko 的一个定理预示了这种可能性。这两个坐标系是 Jacobi 经典节点约化的替代方案，后者例如见于 [V.I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, 18, 85 (1963); p. 141]。
引用
@article{arxiv.1611.00508,
title = {On the co--existence of maximal and whiskered tori for the planetary three--body problem},
author = {Gabriella Pinzari},
journal= {arXiv preprint arXiv:1611.00508},
year = {2018}
}
备注
Accepted peer-reviewed version. 56 pages. Research supported by H2020-ERC Starting Grant 2015 project 677793 "Stable and Chaotic Motions in the Planetary Problem"