Symplectic Geometry and N-body Problem

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The proposal is an extension to the project "Symplectic Geometry and the N-Body Problem". The main purpose is to address diverse problems and research directions of Celestial Mechanics with new methods from symplectic geometry. Within this extension period, we aim to further address the possibility to apply Rabinowitz-Floer theory to study chord problems, in particular consecutive collision orbits in the restricted three-body problems. In the other direction, we wish to address the problem of symmetry in four-body balanced configurations and attempt to obtain results concerning generic finiteness of balanced configurations of N-body problems.