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Title

Frontière du fractal de Rauzy et système de numération complexe

Authors 1

Affiliations

  1. Institut de Mathématiques de Luminy, CNRS-UPR 9016, 163, avenue de Luminy Case 930, 13288 Marseille Cedex 9, France

Bibliography

  1. P. Arnoux, Un exemple de semi-conjugaison entre un échange d'intervalles et une rotation sur le tore, Bull. Soc. Math. France 116 (1988), 489-500.
  2. M. Barnsley, Fractals Everywhere, Academic Press, 1988.
  3. A. Benedek and R. Panzone, The set of Gaussian fractions, in: Proc. Second Conf. Math. 'Dr. Antonio A. R. Monteiro' (Bahia Blanca, 1993), 11-40.
  4. M. Berger, Géométrie 2, Cedic/Nathan, 1977.
  5. F. M. Dekking, Recurrent sets, Adv. Math. 44 (1982), 78-104.
  6. W. J. Gilbert, Complex numbers with three radix expansions, Canad. J. Math. 34 (1982), 1335-1348.
  7. W. J. Gilbert, Fractal geometry derived from complex bases, Math. Intelligencer 4 (1982), 78-86.
  8. W. J. Gilbert, Fractal dimension of sets derived from complex bases, Canad. Math. Bull. 29 (1986), 495-500.
  9. J. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 5 (1981), 713-747.
  10. S. Ito and M. Kimura, On the Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991), 461-486.
  11. S. Ito and M. Mizutani, Potato exchange transformations with fractal domains, preprint.
  12. J. Kátai and J. Szabó, Canonical number systems for complex integers, Acta Sci. Math. (Szeged) 37 (1975), 255-260.
  13. D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, Addison-Wesley, Reading, MA, 1981.
  14. O. Lehto, Univalent Functions and Teichmüller Spaces, Springer, 1986.
  15. A. Messaoudi, Autour du fractal de Rauzy, Thèse de l'Université de la Méditérannée, Aix-Marseille II, 1996.
  16. A. Messaoudi, Propriétés arithmétiques et dynamiques du fractal de Rauzy, J. Théor. Nombres Bordeaux 10 (1998), 135-162.
  17. G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178.
  18. G. Rote, Sequences with subword complexity 2n, J. Number Theory 46 (1972), 196-213.
  19. V. Sirvent, Properties of geometrical realisations of substitutions associated to a family of Pisot numbers, Ph.D. thesis, Univ. of Warwick, 1993.
  20. W. P. Thurston, Groups, tilings, and finite state automata, AMS Colloquium lectures, 1990.
Acta Arithmetica
2000/95/3
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Pages:
195-224
Main language of publication
French
Received
1997-10-27
Accepted
2000-02-01
Published
2000
Exact and natural sciences