How can Semantic Pointer Architecture be used to capture dynamical systems? Most uses of SPA I've seen seem to be representing static systems, such as recognizing digits, categorizing images, rapid variable creation (also called "completing a pattern") and planning a path for writing those digits back out. Can it be used to represent dynamics as well, such as the general movement from a series of images?
As explained in the NEF book, all non-linear dynamical systems can be represented in the NEF.

The SPA is simply applying semantic meaning and manipulations to the vectors represented by the NEF. The two most prominent examples of this are the motor system and the inference system in Spaun, which are shown in the aforementioned "rapid variable creation" task.

The vision system represents symbols (numbers) which get sent to the inference system. The inference system figures out the answer and sends it to the motor system. The motor system converts the symbol to a path and follows it.

Adding dynamics in a similar system with dynamics being visually identified, manipulated and then output, instead of static paths. One could imagine a system where the dynamics of the movement of an object are identified, manipulated neurally and then imitated. For example, having the running of a cheetah represented a series of limb movements, mapping them onto the human body and then having a human imitate that gait.

Of course this hasn't been implemented yet (and would look quite silly), but it shouldn't be super difficult. The main problem would be a good "demo" or psychological data to match, but I think this is still a good example.