2 problems

Local hyperbolization conjecture. There exists a function $\tilde f\in\mathcal{N}$ such that $p$ is a hyperbolic periodic solution of the equation with nonlinearity $\tilde f$.

Generic density conjecture. For any $A>0$ and $K$, ${\cal G}_{2}(3A/2,K)$ is dense in ${\cal G}_{3/2}(3A/2,K)\cap {\cal G}_{2}(A,K)$.