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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 4, Pages 3–26 (Mi izv6596)  

On almost-periodic points of a topological Markov chain

S. A. Bogatyia, V. V. Redkozubovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Institute of Physics and Technology

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.

Keywords: transitive topological Markov chain, periodic point, almost-periodic point, minimal set.

DOI: https://doi.org/10.4213/im6596

Full text: PDF file (572 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:4, 647–668

Bibliographic databases:

UDC: 517.939.5+519.142.1
MSC: Primary 60J05; Secondary 60J20
Received: 30.12.2010
Revised: 21.11.2011

Citation: S. A. Bogatyi, V. V. Redkozubov, “On almost-periodic points of a topological Markov chain”, Izv. RAN. Ser. Mat., 76:4 (2012), 3–26; Izv. Math., 76:4 (2012), 647–668

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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