论文标题
泰特同源性和动力蝇bys
Tate Homology and Powered Flybys
论文作者
论文摘要
在本文中，我们表明，在平面循环限制的三个身体问题中，对于所有能量以下的所有能量低于第一个临界能量值，都有无限的对称连续碰撞轨道，或者至少有一个周期性对称的对称碰撞轨道。使用LEVI-CIVITA正则化使我们能够区分两种不同类型的对称连续碰撞轨道，并分别证明上述主张，一个对应于日食，另一个对应于日食。通过将轨道解释为两个不同的拉格朗日式submanifolds之间的哈密顿和弦，我们可以使用$ g $ equivariant lagrangian lagrangian ragangian ragangian lagrangian ragangian ragangian floer同源性的扰动版本来证明存在这种连续的碰撞轨道。为了计算此同源性，我们表明在某些条件下，$ g $ equivariant lagrangian ragangian raganowitz浮子同源性等于$ g $的TATE同源性。
In this paper we show that in the planar circular restricted three body problem there are either infinitely many symmetric consecutive collision orbits or at least one periodic symmetric consecutive collision orbit for all energies below the first critical energy value. Using Levi-Civita regularization allows us to distinguish two different kinds of symmetric consecutive collision orbits and prove the above claim for both of them separately, one corresponding to a solar eclipse and the other to a lunar eclipse. By interpreting the orbits as Hamiltonian chords between two different Lagrangian submanifolds we can use a perturbed version of $G$-equivariant Lagrangian Rabinowitz Floer homology to prove the existence of this kind of consecutive collision orbit. To calculate this homology we show that under certain conditions the $G$-equivariant Lagrangian Rabinowitz Floer homology is equal to the Tate homology of $G$.
