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

M. I. Malkin1

AnnotationWe 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.
Keywordstopological Markov chains, topological entropy, shift map

1Associate Professor, Department of Differential Equations and Mathematical Analysis, Nizhny Novgorod State Lobachevsky Universit, Nizhny Novgorod; malkin@unn.ru.

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)