Reference Request: Overlaps between complexity theory and dynamical systems? Per Wikipedia:


  In mathematics, a dynamical system is a system in which a function
  describes the time dependence of a point in a geometrical space.
  Examples include the mathematical models that describe the swinging of
  a clock pendulum, the flow of water in a pipe, and the number of fish
  each springtime in a lake.
  
  At any given time a dynamical system has a state given by a set of
  real numbers (a vector) that can be represented by a point in an
  appropriate state space (a geometrical manifold). The evolution rule
  of the dynamical system is a function that describes what future
  states follow from the current state. Often the function is
  deterministic; in other words, for a given time interval only one
  future state follows from the current state however, some
  systems are stochastic, in that random events also affect the
  evolution of the state variables.


Is there any result on dynamical system (i.e. solving dynamical equations, finding asymptotic states to a system, dynamics in chaotic system) with complexity theory, hardness for finding a solution, etc.?

Thanks
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.