dynamics over finite fields. dynamics over function fields such as C(x). iteration of formal and p-adic power series. dynamics on Lie groups. arithmetic properties of dynamically defined moduli spaces. equidistribution[12] and invariant measures, especially on p-adic spaces. dynamics on Drinfeld modules. number-theoretic iteration problems that are not described by rational maps on varieties, for example, the Collatz problem. symbolic codings of dynamical systems based on explicit arithmetic expansions of real numbers.[13]