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On Markoff's property and Sturmian words

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References

  1. Arnoux, P.: Sturmian sequences. In: N. Pytheas-Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics, Lecture Notes in Mathematics 1794, Springer, Berlin Heidelberg, 2002, pp. 143–198

  2. Allouche, J.-P., Shallit, J.: Automatic sequences. Cambridge: Cambridge University Press, 2003

  3. Bernoulli, J.: Sur une nouvelle espèce de calcul. Recueil pour les Astronomes I, 255–284, Berlin, 1772

  4. Borel, J.-P., Laubie, F.: Quelques mots sur la droite projective réelle. Journal de Thérorie des Nombres de Bordeaux 5, 23–51 (1993)

    MATH  MathSciNet  Google Scholar 

  5. Berstel, J., Séébold, P.: Sturmian words, in: M. Lothaire, Algebraic Combinatorics on words. Cambridge: Cambridge University Press, 2002, Chapter 2

  6. Cassaigne, J.: Limit values of the recurrence quotient of Sturmian sequences. Theoretical Computer Science 218, 3–12 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cusick, T.W., Flahive, M.E.: The Markoff and Lagrange spectra. American Mathematical Society, 1989

  8. Christoffel, E.B.: Observatio arithmetica. Annali di Matematica 6, 145–152 ( 1875)

    Google Scholar 

  9. Christoffel, E.B.: Lehrsätze über arithmetische Eigenschaften du Irrationnalzahlen. Annali di Matematica Pura ed Applicata, Series II 15, 1888, pp. 253–276

  10. Dickson, L.E.: Studies in the theory of numbers. Chelsea, New York, 1930 (second edition 1957)

  11. Heinis, A.: Arithmetics and Combinatorics of Words of Low Complexity. Ph D, University of Leiden, 2001

  12. Markoff, A.A.: Sur les formes quadratiques binaires indéfinies. Math. Ann. 15, 381–496 (1879)

    Article  MATH  Google Scholar 

  13. Markoff, A.A.: Sur les formes quadratiques binaires indéfinies (second mémoire). Math. Ann. 17, 379–399 (1880)

    Article  MATH  MathSciNet  Google Scholar 

  14. Markoff, A.A.: Sur une question de Jean Bernouilli. Math. Ann. 19, 27–36 (1882)

    Article  MathSciNet  Google Scholar 

  15. Morse, M., Hedlund, G.A.: Symbolic dynamics II: Sturmian Trajectories. Amer. J. Math. 62, 1–42 (1940)

    Article  MATH  MathSciNet  Google Scholar 

  16. Perron, O.: Über die Approximationen irrationaler Zahlen durch rationale. Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Abhandlungen, 8, 1921

  17. Smith, H.J.S.: Note on continued fractions. Messenger Math. 6, 1–14 (1876)

    Google Scholar 

  18. Yasutomi, S.-I.: The continued fraction expansion of α with μ(α) = 3. Acta Arithmetica 84, 337–374 (1998)

    MATH  MathSciNet  Google Scholar 

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  1. Département de mathématiques, Université du Québec à Montréal, Case postale 8888, succursale Centre-Ville, Montréal (Québec), Canada, H3C 3P8

    Christophe Reutenauer

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  1. Christophe Reutenauer
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Correspondence to Christophe Reutenauer.

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Supported by NSERC.

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Reutenauer, C. On Markoff's property and Sturmian words. Math. Ann. 336, 1–12 (2006). https://doi.org/10.1007/s00208-005-0677-8

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