Decomposition of non-wandering set for non-transitive countable topological Markov chains

We consider the counting topological Markov chain, in general, non-transitive. It is shown that non-wandering set of the map shift by shrinking space orbits is represented as a disjoint union of non-wandering set of transitive component plus perhaps one stable fixed point – symbolic infinity. As a corollary, we obtain the result of the approximation topological entropy decomposable countable topological Markov chain.