7 problems

Let $\Gamma^{\ast}(s)$, $s\geq 0$, denote a triple-collision shape curve, and let the equator circle be the locus representing the first eclipse. Triple-collision shape-curve conje…

Let $P=\Delta+V-\lambda^2$ be the Helmholtz operator on $\mathbb{R}^n$, where $\lambda^2>0$ and $V=\sum_{\alpha\in I}\pi_\alpha^*(V^\alpha)$ is a three-body potential with…

Alekseev's dense collision-orbit conjecture. Is there an open subset $\mathcal{U}$ of the phase space such that for a dense subset of initial conditions the associated trajectories…

Consider the homogeneous potential with exponent $\alpha$ as above, and the moment of inertia $I$. The exceptional exponents are $\alpha=-2$ and $\alpha=2$; the equal-mass rectilin…

Let $N$ point particles have masses $m_k>0$ and positions $\bi{q}_k$, with homogeneous potential … for $\alpha\ne0$. Define the moment of inertia and configurational measure by … A…

Let three equal masses be released from rest in a scalene triangular configuration whose side lengths satisfy … Let $r_{ij}(t)$ be the distance between masses $i$ and $j$, and let…

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…