I don’t think you’re remotely correct, but I also don’t know how to dispute your ignorance in any useful way.

To @esafak I suggest following @westurner’s post.

I like the concept of Stable Manifolds. Classifying types of them is interesting. Group symmetries on the phase space are interesting. Explaining this and more is not work I’m prepared to do here. Use Wikipedia, ask ChatGPT, enrol in a course on Chaos and Fractal Dynamics, etc.