Non-schubart periodic orbits in the rectilinear three-body problem

In the present paper, in the rectilinear three-body problem, we qualitatively follow the positions of non-Schubart periodic orbits as the mass parameter changes. This is done by constructing their characteristic curves. In order to construct characteristic curves, we assume a set of properties on the shape of areas corresponding to symbol sequences. These properties are assured by our preceding numerical calculations. The main result is that characteristic curves always start at triple collision and end at triple collision. This may give us some insight into the nature of periodic orbits in the N-body problem.