Reference Request: Overlaps between complexity theory and dynamical systems?
This is a well-researched area. For a representative result, see Kawamura's proof that solving ODEs is difficult.

A different line of works studies the hardness of computing Nash equilibria and related problems. See for example the recent breakthrough of Bitansky, Paneth and Rosen, who base hardness of cryptographic assumptions; earlier work based it on complexity theoretic assumptions.