Topology provides a new way of analyzing dynamical systems. Using what is called a Poincar section, along with some other high-powered mathematics, we can visualize the behavior of dynamical systems in an entirely new sense. However, I will mention the strange attractor . Loosely, an attractor is what a function eventually settles down to. Any other attractor is as strange attractor.
Strange attractors are extremely complex, and they describe extremely complex behavior.
Poincar s work hinted that simple nonlinear dynamical systems could produce very complex behavior. Simple nonlinear dynamical systems settled down to strange attractors. All of this is theoretical mathematical material, and it was viewed as merely such by the scientific world for more than half a century. It was not in any manner related to physics or any other real-world science. This makes sense, in linear dynamical systems .