2020/05/11 by Kopra, Johan
#37B15 (Primary) 37B10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.05112
We address the dynamics of the cellular automaton (CA) that multiplies by p/q in base pq (for coprime p>q>1) by studying its trace subshift. We present a conjugacy of the trace to a previously studied base-p/q numeration system. We also show that the trace subshift is not synchronizing and in particular not sofic. As a byproduct we compute its complexity function and we conclude by presenting an example of a sofic shift with the same complexity function.