6 problems

Triangular existence classification conjecture. There exist $\kappa_4(\mu)<\kappa_5(\mu)$ in $(0,\pi^2/4)$ such that there are two triangular relative equilibria,…

Existence classification conjecture. There exist $\kappa_i=\kappa_i(\mu)\in(0,\pi^2/4)$ with $\kappa_1<\kappa_2<\kappa_3$ such that the curved restricted three-body problem has exa…

Consider a balanced family in the three-body problem in $\mathbb{R}^4$, with functions $h$ and $k$ defined along the family. Critical-point conjecture. On each balanced family, the…

Let a balanced configuration of the three-body problem in $\mathbb{R}^4$ have angular momentum $L$ and eigenvalues $\mu_1$ and $\mu_2$. Uniqueness conjecture. For any choice of mas…

Consider the N-body problem with general positive masses and its relative equilibria, namely solutions generated by central configurations. The first excited state is the relative…

Consider the Newtonian $N$-body problem, with potential corresponding to $\alpha=1$, and let $I$ be the moment of inertia. A motion has constant moment of inertia when $I$ is const…