椭圆三体问题中的时间周期不变流形

Time-Periodic Invariant Manifold in the Elliptic Three Body Problem

借助有限时间Lyapunov指数(FTLE)定义拉格朗日拟序结构(LCS),并以单摆系统为例阐述LCS与动力系统中不变流形之间的联系.利用LCS研究椭圆限制性三体问题(ER3BP)中的时间周期不变流形的性质.采用数值方法验证得到了两点结论:时间周期不变流形的内部是穿越轨道集,外部是非穿越轨道集;时间周期不变流形是轨道的不变集.

Lagrangian coherent structure（LCS） is defined by means of ridges of finite-time Lyapunov exponent（FTLE） fields in this paper.Moreover,a relation between LCS and time-dependent invariant manifold is obtained.Taking LCS as a tool,the property of the invariant manifold in elliptic restricted 3-body problem（ER3BP） is achieved numerically： time-dependent invariant manifold is an invariant set of orbits and acts as the separatrix of transit-orbit set and non-transit orbit set.