| Abstract: |
| We prove the existence of periodic brake orbits in the planar pairwise symmetric four-body problem with equal masses and full symmetry among the four bodies. These singular periodic brake orbits experience at least one brake and at least two distinct regularizable simultaneous binary collisions per period. The analytic existence of these singular periodic brake orbit are based on differential inequalities, qualitative techniques, and the gradient-like flow on the total collision manifold obtained from McGehee regularization. |
|