Frontière du fractal de Rauzy et système de numération complexe

Ali Messaoudi

Acta Arithmetica (2000)

  • Volume: 95, Issue: 3, page 195-224
  • ISSN: 0065-1036

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Messaoudi, Ali. "Frontière du fractal de Rauzy et système de numération complexe." Acta Arithmetica 95.3 (2000): 195-224. <http://eudml.org/doc/207448>.

@article{Messaoudi2000,
author = {Messaoudi, Ali},
journal = {Acta Arithmetica},
keywords = {Rauzy fractal; quasi-circle; Hausdorff dimension; strictly extreme points; convex hull; symbolic dynamics},
language = {fre},
number = {3},
pages = {195-224},
title = {Frontière du fractal de Rauzy et système de numération complexe},
url = {http://eudml.org/doc/207448},
volume = {95},
year = {2000},
}

TY - JOUR
AU - Messaoudi, Ali
TI - Frontière du fractal de Rauzy et système de numération complexe
JO - Acta Arithmetica
PY - 2000
VL - 95
IS - 3
SP - 195
EP - 224
LA - fre
KW - Rauzy fractal; quasi-circle; Hausdorff dimension; strictly extreme points; convex hull; symbolic dynamics
UR - http://eudml.org/doc/207448
ER -

References

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  2. [2] M. Barnsley, Fractals Everywhere, Academic Press, 1988. 
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  4. [4] M. Berger, Géométrie 2, Cedic/Nathan, 1977. 
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  6. [6] W. J. Gilbert, Complex numbers with three radix expansions, Canad. J. Math. 34 (1982), 1335-1348. Zbl0478.10007
  7. [7] W. J. Gilbert, Fractal geometry derived from complex bases, Math. Intelligencer 4 (1982), 78-86. Zbl0493.10010
  8. [8] W. J. Gilbert, Fractal dimension of sets derived from complex bases, Canad. Math. Bull. 29 (1986), 495-500. Zbl0564.10007
  9. [9] J. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 5 (1981), 713-747. Zbl0598.28011
  10. [10] S. Ito and M. Kimura, On the Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991), 461-486. Zbl0734.28010
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  13. [13] D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, Addison-Wesley, Reading, MA, 1981. Zbl0477.65002
  14. [14] O. Lehto, Univalent Functions and Teichmüller Spaces, Springer, 1986. 
  15. [15] A. Messaoudi, Autour du fractal de Rauzy, Thèse de l'Université de la Méditérannée, Aix-Marseille II, 1996. 
  16. [16] A. Messaoudi, Propriétés arithmétiques et dynamiques du fractal de Rauzy, J. Théor. Nombres Bordeaux 10 (1998), 135-162. Zbl0918.11048
  17. [17] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. Zbl0522.10032
  18. [18] G. Rote, Sequences with subword complexity 2n, J. Number Theory 46 (1972), 196-213. Zbl0804.11023
  19. [19] V. Sirvent, Properties of geometrical realisations of substitutions associated to a family of Pisot numbers, Ph.D. thesis, Univ. of Warwick, 1993. 
  20. [20] W. P. Thurston, Groups, tilings, and finite state automata, AMS Colloquium lectures, 1990. 

Citations in EuDML Documents

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  1. Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry, Geometric study of the beta-integers for a Perron number and mathematical quasicrystals
  2. Anne Siegel, Système dynamique à spectre discret et pavage périodique associé à une substitution
  3. Valérie Berthé, Timo Jolivet, Anne Siegel, Connectedness of fractals associated with Arnoux–Rauzy substitutions
  4. Pierre Arnoux, Valérie Berthé, Shunji Ito, Discrete planes, 2 -actions, Jacobi-Perron algorithm and substitutions
  5. Nataliya Chekhova, Pascal Hubert, Ali Messaoudi, Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci
  6. Jörg M. Thuswaldner, Unimodular Pisot substitutions and their associated tiles
  7. Julien Cassaigne, Sébastien Ferenczi, Luca Q. Zamboni, Imbalances in Arnoux-Rauzy sequences
  8. Pierre Arnoux, Valérie Berthé, Arnaud Hilion, Anne Siegel, Fractal representation of the attractive lamination of an automorphism of the free group
  9. Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner, Dynamical directions in numeration

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