classical mechanics - Do unstable equilibria lead to a violation of Liouville's theorem?

Liouville's theorem says that the flow in phase space is like an incompressible fluid. One implication of this is that if two systems start at different points in phase space their phase-space trajectories cannot merge. But for a potential with an unstable equilibrium, I think I've found a counterexample.

Consider the potential below (excuse bad graphic design skills).

A particle starting at rest at point A, $(q,p) = (x_A,0)$ at $t = 0$, would accelerate down the potential towards the left. Because it has the amount of energy indicated by the purple line, it would come to rest at the local maximum B at $t = T$, an unstable equilibrium $(q,p) = (x_B,0)$. However any particle started at rest at the top of the local maximum B at $t = 0$ would also stay that way forever, including up to $t = T$. Thus there appears to be two trajectories that merge together in violation of Liouville's thorem.