Factor maps, entropy and fiber cardinality for Markov shifts (Q1596559)

Let \(S:S\rightarrow S\) and \(T:T\rightarrow T\) be two locally compact transitive Markov shifts, which are a generalization of subshifts of finite type relaxing the compacity condition (as in the paper we identify the map and the space). A factor map \(f:S\rightarrow T\) is a continuous surjective map such that \(T\circ f=f\circ S\). The Gurevic entropy of \(S\) is defined to be the topological entropy of the natural extension \(S^*\) defined on the one-point compactification of \(S\). The author studies the relationship between different types of factor maps (depending on the cardinality of preimages of points of \(T\)) and the Gurevic entropies of \(S\) and \(T\).