The continued fraction expansion of α with μ(α) = 3

Shin-Ichi Yasutomi

Acta Arithmetica (1998)

  • Volume: 84, Issue: 4, page 337-374
  • ISSN: 0065-1036

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Shin-Ichi Yasutomi. "The continued fraction expansion of α with μ(α) = 3." Acta Arithmetica 84.4 (1998): 337-374. <http://eudml.org/doc/207148>.

@article{Shin1998,
author = {Shin-Ichi Yasutomi},
journal = {Acta Arithmetica},
keywords = {continued fraction expansion; Lagrange spectrum; Markov spectrum; Bernoulli sequence; super Bernoulli sequence},
language = {eng},
number = {4},
pages = {337-374},
title = {The continued fraction expansion of α with μ(α) = 3},
url = {http://eudml.org/doc/207148},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Shin-Ichi Yasutomi
TI - The continued fraction expansion of α with μ(α) = 3
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 4
SP - 337
EP - 374
LA - eng
KW - continued fraction expansion; Lagrange spectrum; Markov spectrum; Bernoulli sequence; super Bernoulli sequence
UR - http://eudml.org/doc/207148
ER -

References

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  1. [1] H. Cohn, Some direct limits of primitive homotopy words and of Markoff geodesics, in: Discontinuous Groups and Riemann Surfaces, Univ. of Maryland, 1973, Ann. of Math. Stud. 79, Princeton, 1974, 91-98. 
  2. [2] T. W. Cusick and M. E. Flahive, The Markoff and Lagrange Spectra, Math. Surveys Monographs 30, Amer. Math. Soc., Providence, 1989. Zbl0685.10023
  3. [3] S. Ito and S. Yasutomi, On continued fraction, substitution and characteristic sequences [nx + y] - [(n-1)x + y], Japan. J. Math. 16 (1990), 287-306. Zbl0721.11009
  4. [4] W. F. Lunnon and A. B. Pleasants, Characterization of two-distance sequences, J. Austral. Math. Soc. Ser. A 53 (1992), 198-218. Zbl0759.11005
  5. [5] A. Markoff [A. Markov], Sur les formes quadratiques binaires indéfinies, Math. Ann. 15 (1879), 381-406; II, Math. Ann.. 17 (1880), 379-399. 
  6. [6] A. Markoff [A. Markov], Sur une question de Jean Bernoulli, Math. Ann.. 19 (1882), 27-36. 
  7. [7] M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math 62 (1940), 1-42. Zbl0022.34003
  8. [8] I. Nakashima, J. Tamura and S. Yasutomi, Modified complexity and *-Sturmian word, preprint, 1997. Zbl0928.11012
  9. [9] O. Perron, Die Lehre von den Kettenbrüchen I, Teubner, Stuttgart, 1954. Zbl0056.05901
  10. [10] A. M. Rocket and P. Szüsz, Continued Fractions, World Scientific, 1992. 

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