Not really. It's a dome/hill shape, not a saddle, and nothing in particular goes to infinity. The only thing special about the shape is that it's constructed such that there exists a way to kick a ball straight up the slope and (if you're impossibly precise), it'll come to rest at the top in finite time.

This in itself is fine, but starts feeling real weird once you are familiar with the time-reversability of physical systems. If you time-reverse this system, you end up with a ball that sits at the top for an arbitrary period of time, and then suddenly just rolls down for no deterministic reason.

If you considered a bunch of different runs of this, some where the ball starts at the top, stationary, and some where it's kicked up to stop at the top (from various locations, at various times), they all start at the exact same conditions in the time-reversed system. So why do they do different, unpredictable things?