3 problems

Let $V$ be a potential and let $E$ be an energy such that $V^{-1}((-infty,E])$ is homeomorphic to an $n$-dimensional disk. A brake orbit is a pendulum-like periodic solution of the…

Assume a brake orbit segment in the three-body problem, beginning at brake time and ending at its first syzygy. Let $I(t)$ denote the total moment of inertia of the three bodies. M…

Let $n\geq 2$, and let $\Sigma$ range over the class $\mathcal{H}_b^{c}(2n)$ of compact convex hypersurfaces with the brake symmetry considered in the source. Write…