Embedding theorems for locally compact Markov shifts

Abstract

We characterize when a lower entropy locally compact subshift S embeds into a locally compact mixing Markov shift T. As in the compact case (when T is a shift of finite type) the existence of an embedding depends on S only through its periodic orbit counts. However, in contrast to the compact case, the topology of the target system T becomes important. This is demonstrated with the help of the Zeta Function Lemma, which in particular characterizes the periodic orbit counts and entropies of locally compact mixing Markov shifts.