Computability of Dynamical Systems

Computational models of nature often take the form of dynamical systems. Sometimes, these systems exhibit solutions which are chaotic and notoriously difficult to compute. One important example is turbulent solutions of the Navier-Stokes equations. Another example is the Lorenz system, a seemingly simple system of three ordinary differential equations with chaotic solutions. We are currently investigating and quantifying the computability of some simple dynamical systems with a particular focus on long-time predictability and computability.