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Uspekhi Mat. Nauk, 2009, Volume 64, Issue 5(389), Pages 21–96 (Mi umn9315)  

This article is cited in 13 scientific papers (total in 13 papers)

Sequences close to periodic

An. A. Muchnika, Yu. L. Pritykinb, A. L. Semenovc

a Institute for New Technology in Education, Moscow
b M. V. Lomonosov Moscow State University
c Dorodnitsyn Computing Centre of the Russian Academy of Sciences

Abstract: This paper is a survey of concepts and results connected with generalizations of the notion of a periodic sequence, both classical and new. The topics discussed relate to almost periodicity in such areas as combinatorics on words, symbolic dynamics, expressibility in logical theories, computability, Kolmogorov complexity, and number theory.
Bibliography: 124 titles.

Keywords: combinatorics on words, symbolic dynamics, decidability of logical theories, almost periodic sequence, morphic sequence, Thue–Morse sequence, complexity of a sequence, Sturmian sequences.

DOI: https://doi.org/10.4213/rm9315

Full text: PDF file (1239 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2009, 64:5, 805–871

Bibliographic databases:

UDC: 510.5+510.6+519.101+517.938
MSC: 03-02, 03B25, 03D03, 03D05, 03D40, 05-02, 05A05, 11B50, 11B75, 11B85, 11J82, 20F10, 37B10, 37B40, 68Q30, 68Q45, 68Q70, 68R15
Received: 07.08.2009

Citation: An. A. Muchnik, Yu. L. Pritykin, A. L. Semenov, “Sequences close to periodic”, Uspekhi Mat. Nauk, 64:5(389) (2009), 21–96; Russian Math. Surveys, 64:5 (2009), 805–871

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. N. Korneeva, “Automaton transformations and monadic theories of infinite sequences”, Russian Math. (Iz. VUZ), 55:8 (2011), 78–80  mathnet  crossref  mathscinet  elib
    2. Prunescu M., “The Thue–Morse–Pascal double sequence and similar structures”, C. R. Math. Acad. Sci. Paris, 349:17-18 (2011), 939–942  crossref  mathscinet  zmath  isi  scopus
    3. A. M. Vershik, “The Pascal automorphism has a continuous spectrum”, Funct. Anal. Appl., 45:3 (2011), 173–186  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M. N. Vyalyi, A. A. Rubtsov, “Algoritmicheskaya razreshimost zadach o povedenii avtomatov na sverkhslovakh”, Diskretn. analiz i issled. oper., 19:2 (2012), 3–18  mathnet  mathscinet
    5. N. N. Korneeva, “Monadicheskie teorii posledovatelnostei pri asinkhronno avtomatnykh preobrazovaniyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 117–124  mathnet
    6. M. Prunescu, “$\mathbb F_p$-affine recurrent $n$-dimensional sequences over $\mathbb F_q$ are $p$-automatic”, European J. Combin., 34:2 (2013), 260–284  crossref  mathscinet  zmath  isi  elib  scopus
    7. L. Kulesa, “Equivalence of Right Infinite Words”, Journal of Discrete Mathematics, 2013 (2013), 219291, 8 pp.  crossref  zmath
    8. Batkhin A.B., “Symmetric Periodic Solutions of the Hill's Problem. I”, Cosmic Res., 51:4 (2013), 275–288  crossref  adsnasa  isi  elib  scopus
    9. I. V. Mitrofanov, “Periodicity of morphic words”, J. Math. Sci., 206:6 (2015), 679–687  mathnet  crossref  mathscinet
    10. N. N. Korneeva, “Automata transformations of prefix decidable and decidable by Buchi superwords”, Russian Math. (Iz. VUZ), 60:7 (2016), 47–55  mathnet  crossref  isi
    11. Lavrov P.A., “Specifying periodic words by restrictions”, Dokl. Math., 93:3 (2016), 300–303  crossref  mathscinet  zmath  isi  elib  scopus
    12. Mitrofanov I.V., “On almost periodicity of morphic sequences”, Dokl. Math., 93:2 (2016), 207–210  crossref  mathscinet  zmath  isi  elib  scopus
    13. Davydova M.G., Korolenko P.V., Ryzhikova Yu.V., “The stability of the fractal properties of quasiperiodic multilayered structures”, Mosc. Univ. Phys. Bull., 71:4 (2016), 395–399  crossref  isi  elib  scopus
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