[stonesixone]

My memory may be a bit fuzzy on this. But I believe one way the term "dynamics" is used in her work is in reference to the space of Riemann surfaces (or equivalently, the space of hyperbolic geometries on a surface). This space is called moduli space. Certain topological operations on the surface (e.g. twisting a "handle") give rise to a corresponding transformation on moduli space. So one of the things mathematicians in this area can study is the dynamics of such operations on moduli space. This means, for example, studying the behavior of these operations on moduli space, in the limit.

Also, to a mathematician, "dynamics" can often simply mean studying the behavior of iterations of a single function from a space to itself. So the parameter "t" in this case is over the positive integers (or all integers if the function has an inverse).