Decomposition of non-wandering set for non-transitive countable topological Markov chains
M. I. Malkin1
|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.
|topological Markov chains, topological entropy, shift map
1Associate Professor, Department of Differential Equations and Mathematical Analysis, Nizhny Novgorod State Lobachevsky Universit, Nizhny Novgorod; firstname.lastname@example.org.
Citation: M. I. Malkin, "[Decomposition of non-wandering set for non-transitive countable topological Markov chains]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,15:2 (2013) 49–54 (In Russian)