Factor theorems for locally compact Markov shifts II

Abstract

Let S and T be locally compact transitive countable state Markov shifts. When is there a factor map from S onto T? In the compact setting a trivial periodic point condition and the topological entropy settle this question. For the non-compact case the behaviour of the Markov shifts at infinity plays a central role. To capture some of this we introduce a new entropy at infinity and use it to solve the factoring problem in several situations.