Non-wandering set

Imagine you're playing a game where you're jumping on a trampoline. Sometimes you jump really high and go all around the trampoline, but other times you kind of stay in one spot and just bounce a little. The non-wandering set in math is kind of like the spots on the trampoline where you bounce a little - they're the points that don't move around a lot.

In more technical terms, the non-wandering set is a set of points in a mathematical system where if you start at a point in that set, you'll end up staying in that set forever. Think of it like a circle on a map - if you start at a point on the circle and keep going around and around, you'll always end up back at another point on the circle.

So basically, the non-wandering set is just the points in a system that don't move around a lot - they kind of stay put, and if you start at one of those points, you'll keep going around and around that set without ever leaving it. Cool, huh?