Morse nondegeneracy conjecture for heteroclinic-orbit flows

Let $\mathcal{H}$ be the space of heteroclinic orbits of the flow associated with

$$. **Morse nondegeneracy conjecture.** When the flow of$$

is restricted to $\mathcal{H}$, all equilibria become nondegenerate critical points in the sense of Morse. Such nondegeneracy would remove a principal obstacle to constructing a Floer homology for the space of heteroclinic orbits, but the source leaves the assertion open.