Geodesic
Sequences close to periodic
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 5, pp. 805-871

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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. 
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An. A. Muchnik; Yu. L. Pritykin; A. L. Semenov. Sequences close to periodic. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 5, pp. 805-871. http://geodesic.mathdoc.fr/item/RM_2009_64_5_a1/