Generic density of hyperbolic periodic solutions for scalar parabolic equations

Let ${\cal G}_{3/2}(3A/2,K)$ and ${\cal G}_{2}(A,K)$ be the classes of nonlinearities represented by these sets, for any $A>0$ and $K$.

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

The authors state that proving this density result would yield genericity of the Kupka–Smale property; the conjecture is presented as an unresolved step in the proof of generic hyperbolicity.