5 problems

Collinear stability classification conjecture. $\operatorname{L}_1,\operatorname{L}_2,\operatorname{E}_3$, and $\operatorname{A}_1$ are center-saddles whenever they exist;…

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…

Persistence conjecture. For every small $e>0$ there exists $\mu(e)$ for which the orbit $L_1$ has a homoclinic orbit. Moreover, there is a neighborhood $U$ of the curve…

Alekseev's conjecture. The set $OM$ has Lebesgue measure zero.