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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?

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  • $\begingroup$ They claim dynamical systems are applied mathematics at the 4:44 minute mark in the video, not pure. Are you sure you aren't confusing it with something else in the video? $\endgroup$ Sep 14, 2017 at 13:16
  • $\begingroup$ I have already downloaded the video, At 4.44 minute mark he tells about Topology. At 5.30 he speak about Dynamical systems. $\endgroup$
    – user158
    Sep 15, 2017 at 12:05
  • $\begingroup$ Apparently I mean 6:44, not 4:44. It seems they mention dynamical systems twice, both in pure and applied but right after the 5:30 section he mentions that many of these subjects have overlap with applied topics. $\endgroup$ Sep 15, 2017 at 14:25

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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.

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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.

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All Mathematics is pure until you use it to solve another problem (i.e., apply it to that problem).

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For whatever it’s worth, in some countries (e.g., Germany) dynamical systems is considered a subfield of physics by some. Roughly half the people working on dynamical systems in those countries are physicists. I did my PhD in physics on dynamical systems.

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