A difference variety is equipped with a self-map, and the connection to dynamical systems is (at least ‘a posteriori’) not too surprising. The idea of Poonen, explained in the paper by Fakhruddin, shows how the twisted Lang–Weil estimates of Hrushovski (and results of Macintyre) for difference varieties over algebraically closed fields equipped with powers of Frobenius can be applied to deduce density (in the Zariski topology) of the set of periodic points on a complex variety with a suitable self-map. We give a significant improvement of these considerations.