Tate Homology and powered Flybys
In this talk, I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value. By using the Levi-Civita regularization we will be able to distinguish between two different orientations of these orbits and prove the above claim for both of them separately. In the first part of the talk, I want to explain the motivation behind this result, especially its connection to powered Flybys. Afterward I will introduce the main technical tools, one needs to prove the above statement, like Lagrangian Rabinowitz Floer Homology and its G-equivariant version. To be able to effectively calculate this G-equivariant Lagrangian RFH, we will relate it to the Tate homology of the group G. With this tool at hand, we will then finally be able to prove that there are infinitely many consecutive collision orbits all facing in a specific direction.