Symbol sequences and orbits of the free-fall three-body problem

Abstract

Using the symbols and symbol sequences along the orbits introduced in our preceding work, we numerically study the orbital structure of the free-fall three-body problem. We confirm and re-interpret the results obtained by us before. We describe the overall structure of the plane. It turns out that the structures of the initial condition plane can be systematically obtained with symbol sequences. Then, we obtain the structure of two interesting local regions: the isosceles and collinear boundaries of the plane. We present sequences of triple collision orbits and periodic orbits on these boundaries. We additionally argue that stable and/or unstable manifolds of the two-body collision manifolds connect different triple collision manifolds.