I found this video where it categorize dynamical systems under pure mathematics. I suppose it is topic under applied mathematics. Is really dynamical systems a topic under pure mathematics? If so why?
IMHO: The distinction between "pure" and "applied" essentially concerns people's motivation for studying the subject. If you want to solve a non-mathematical problem using mathematics, you're applied. If you just like math, you're pure. The topic itself, Dynamical Systems, like most other topics within mathematics, can be both pure and applied.
Some areas of dynamical systems could be categorized under pure mathematics, specifically when one begins discussing topological spaces, set theory, and fractals applicable to the study of dynamical systems. However, dynamical systems can also be categorized under applied mathematics when utilizing methods to understand bifurcation models, population models, and many other real world applications.