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.
I am quite familiar with this space and I will reassert that its by far most significant application is making pretty pictures.
The Wikipedia list you're indirectly referencing is basically a fantasy wishlist of the areas where we expected the chaos theory to revolutionize things, with little to show for it. "Chaos theory cryptography", come on.
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.