Download PDF - Trajectories of rotationsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Trajectories of rotations

Authors 1, 1, 1

Affiliations

  1. Institut de Mathématiques de Luminy, Case 930, 163 avenue de Luminy, F-13288 Marseille Cedex 9, France

Bibliography

  1. [ALL] J. P. Allouche, Sur la complexité des suites infinies, Bull. Belg. Math. Soc. 1 (1994), 133-143.
  2. [ARN-FIS] P. Arnoux and A. Fisher, The scenery flow for geometric structures on the torus, preprint, 1997.
  3. [HED-MOR] G. A. Hedlund and M. Morse, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42.
  4. [ITO-YAS] S. Ito and S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx+y]-[(n-1)x+y], Japan. J. Math. 16 (1990), 287-306.
  5. [KEA] M. Keane, Sur les mesures quasi-ergodiques des translations irrationnelles, C. R. Acad. Sci. Paris 272 (1971), 54-55.
  6. [KOM1] T. Komatsu, Results on fractional parts of linear functions of n and applications to Beattie sequences, Ph.D. thesis, Macquarie University, 1994.
  7. [KOM2] T. Komatsu, On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337-351.
  8. [KOM3] T. Komatsu, A certain power series associated with a Beatty sequence, Acta Arith. 76 (1996), 109-129.
  9. [KOM4] T. Komatsu, A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory 59 (1996), 291-312.
  10. [KOM5] T. Komatsu, The fractional part of nθ + ϕ and Beatty sequences, J. Théor. Nombres Bordeaux 7 (1995), 387-406.
  11. [NIS-SHI-TAM] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of a certain power series, J. Number Theory 42 (1992), 61-87.
  12. [OST] A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximationen I, II, Abh. Math. Sem. Hamburg 1 (1922), 77-98, 250-251.
  13. [RAU1] G. Rauzy, Une généralisation des développements en fractions continues, Sém. Delange-Pisot-Poitou 1976-1977, exp. 15.
  14. [RAU2] G. Rauzy, Mots infinis en arithmétique, in: Lecture Notes in Comput. Sci. 192, Springer, 1985, 165-171.
  15. [RAU3] G. Rauzy, Échanges d'intervalles et transformations induites, Acta Arith. 34 (1979), 315-328.
  16. [SID-VER] N. A. Sidorov and A. M. Vershik, Arithmetic expansions associated with rotations of the circle and continued fractions, St. Petersburg Math. J. 5 (1994), 1121-1136.
  17. [SOS] V. T. Sós, On the distribution of the sequence nα, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 1 (1958), 127-134.
Acta Arithmetica
1998-1999/87/3
Export to PBN, Opens in new tab
Pages:
209-217
Main language of publication
English
Received
1997-02-25
Accepted
1998-06-15
Published
1999
Exact and natural sciences