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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2009 Volume 64, Issue 5(389), Pages 21–96 (Mi rm9315)

This article is cited in 20 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.

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

DOI: 10.4213/rm9315


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

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© Steklov Math. Inst. of RAS, 2024