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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
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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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