Poincaré map

Imagine you're playing with a ball on a bumpy hill. Sometimes the ball goes up, and sometimes it goes down. But every time the ball goes back to the same spot it started, you make a dot with your crayon. You keep doing this every time the ball comes back to its starting spot. After a while, you have a bunch of dots on the paper.

Now, if you connect all the dots with lines, you'll have a map of where the ball goes on the hill! That's what a Poincaré map is. It's a way to show the path of something that moves in a repeating pattern.

Scientists use Poincaré maps to understand how things like planets or atoms move. They use a lot of math, but the basic idea is the same. They make dots on a graph every time the thing they're studying gets back to its starting place, and then they connect the dots to see its path. It helps them learn more about how everything works.