A chaotic dynamical system is a system whose state evolves in time according to a deterministic rule: A system at state x will evolve after one time unit into the state f(x), where f is some specified function. After two time units, the system will arrive to state f(f(x)), after three time units to f(f(f(x))) and so on. For "chaotic" systems, these calculations cannot be done reliably, even with the help of strong computers, because of the phenomenon of sensitivity to initial conditions: The slightest errors in the initial state x, or round-off errors in subsequent steps, can lead to large errors in the prediction of future states very fast.
"Symbolic dynamics" is a technique for simplifying the law of motion by means of a suitable change of coordinates in such a way that it becomes much easier to apply and to study. The technique was applied successfully in special cases in the sixties. In 2013 WIS scientists showed that it can be applied to general "chaotic" differentiable dynamical systems of dimension two.