Once in a lecture, one of my physics teacher mentioned that a system with 3 degrees of freedom or more is capable of exhibiting chaos. This result draws my attention enormously since the number 3 there looks like a "magic number". Later in a tutorial, I asked one of my tutor on how we could really derive this result. And he told me, quite roughly, that this result can be derived from knot theory.
I am currently neither being so familiar with dynamical systems nor with knot theory, so probably it is better to treat this question as a soft question (but technical answers are also warmly welcomed). If what I remember from the tutor is correct, I would be amazed by how dynamical systems could be linked to knot theory, and more generally, to algebra (btw, any insights on how dynamical systems could be linked to algebra are also heartily welcomed).