Stable manifold

Imagine you're playing with a toy car and you want to drive it towards a target. But the surface you're playing on is bumpy and uneven, so the car doesn't always go where you want it to.

Now imagine the car has a magnet underneath it, and the target has another magnet that attracts the car towards it. No matter how bumpy the surface is, the car will eventually end up close to the target because of the magnets.

In math, we call this force that pulls things towards a target a "stable manifold." It's a way of describing how things move around in space and how they end up where they do.

So, when you hear the term "stable manifold" in math, think of it like a magnet that pulls things towards a goal. It's a handy tool for understanding how the world works and predicting what will happen next.