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On almost-periodic points of a topological Markov chain. (English. Russian original) Zbl 1260.60143

Izv. Math. 76, No. 4, 647-668 (2012); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 76, No. 4, 3-26 (2012).
Authors’ abstract: We prove that a transitive topological Markov chain has almost-periodic points of all \(D\)-periods. Moreover, every \(D\)-period is realized by continuously many distinct minimal sets. We give a simple constructive proof of the result which asserts that any transitive topological Markov chain has periodic points of almost all periods, and study the structure of the finite set of positive integers that are not periods.

MSC:

60J05 Discrete-time Markov processes on general state spaces
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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