Mean equicontinuity and amorphic complexity

We investigate the relations of two complexity notions in the zero entropy regime: mean equicontinuity and amorphic complexity. As it turns out, there is a close relationship in the minimal setting and we will present further results highlighting the interplay of these two concepts. Further, for mean equicontinuous subshifts we prove that amorphic complexity corresponds to the box dimension of the maximal equicontinuous factor and for certain Toeplitz subshifts we show how to calculate amorphic complexity using the theory of iterated function systems. If time permits, we will also elaborate on possible extensions of these notions, in particular with respect to more general group actions. This is work in progress with Gabriel Fuhrmann, Tobias Jäger and Dominik Kwietniak.