Hyperbolic fixed point

Okay kiddo, have you ever played a game of tag or duck-duck-goose? Well, imagine you and your friends are playing on a playground, and there's a spot on the ground that's like a magnet for tagging. Every time someone gets close to that spot, they get tagged and have to be "it" for the next round.

That spot on the ground is like a hyperbolic fixed point. It's a point in a system (like a game or equation) where things are constantly moving around it, but always getting pulled back towards it in a very specific way, just like the way your friends keep getting pulled towards that spot on the playground.

The "hyperbolic" part of the name just means that the way things move around the point is kind of like a stretched out version of a circle. It's like if you took the circle of friends running around the playground and pulled it out into more of an oval shape.

Overall, a hyperbolic fixed point is just a special point in a system that's really good at "attracting" things towards it, even as they keep moving around in different ways. It's kind of like a really good hiding spot in a game of hide-and-seek - even if you move around a lot, you always end up back there.