Wrapped Floer homology and the circular restricted three-body problem

TL;DR

This paper employs wrapped Floer homology to establish the existence of consecutive collisions and symmetric periodic orbits in the circular restricted three-body problem at energies just above the first critical value.

Contribution

It introduces a novel application of wrapped Floer homology to prove new dynamical phenomena in the three-body problem.

Findings

Existence of consecutive collisions at primaries.

Existence of symmetric periodic orbits.

Results valid for energy levels slightly above the first critical value.

Abstract

Using the wrapped Floer homology, we prove the existence of consecutive collisions at the primaries in the circular restricted three-body problem. We also prove the existence of a symmetric periodic orbit. These existence results are obtained for energy hypersurfaces slightly above the first critical value.