Trajectories of rotations

Pierre Arnoux; Sébastien Ferenczi; Pascal Hubert

Acta Arithmetica (1999)

  • Volume: 87, Issue: 3, page 209-217
  • ISSN: 0065-1036

How to cite


Pierre Arnoux, Sébastien Ferenczi, and Pascal Hubert. "Trajectories of rotations." Acta Arithmetica 87.3 (1999): 209-217. <>.

author = {Pierre Arnoux, Sébastien Ferenczi, Pascal Hubert},
journal = {Acta Arithmetica},
keywords = {combinatorics on words; Sturmian sequences; continued fraction; Ostrowski algorithm},
language = {eng},
number = {3},
pages = {209-217},
title = {Trajectories of rotations},
url = {},
volume = {87},
year = {1999},

AU - Pierre Arnoux
AU - Sébastien Ferenczi
AU - Pascal Hubert
TI - Trajectories of rotations
JO - Acta Arithmetica
PY - 1999
VL - 87
IS - 3
SP - 209
EP - 217
LA - eng
KW - combinatorics on words; Sturmian sequences; continued fraction; Ostrowski algorithm
UR -
ER -


  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. Zbl0022.34003
  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. Zbl0721.11009
  5. [KEA] M. Keane, Sur les mesures quasi-ergodiques des translations irrationnelles, C. R. Acad. Sci. Paris 272 (1971), 54-55. Zbl0202.33704
  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. Zbl0829.11012
  8. [KOM3] T. Komatsu, A certain power series associated with a Beatty sequence, Acta Arith. 76 (1996), 109-129. Zbl0858.11013
  9. [KOM4] T. Komatsu, A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory 59 (1996), 291-312. Zbl0872.11033
  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. Zbl0770.11039
  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. Zbl0414.28018
  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. Zbl0094.02903

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.