Frontière du fractal de Rauzy et système de numération complexe
Messaoudi, Ali
Acta Arithmetica, Tome 92 (2000), p. 195-224 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207448
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     author = {Messaoudi, Ali},
     title = {Fronti\`ere du fractal de Rauzy et syst\`eme de num\'eration complexe},
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {195-224},
     zbl = {0968.28005},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav95z3p195bwm}
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Messaoudi, Ali. Frontière du fractal de Rauzy et système de numération complexe. Acta Arithmetica, Tome 92 (2000) pp. 195-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav95z3p195bwm/

[000] [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. | Zbl 0703.58045

[001] [2] M. Barnsley, Fractals Everywhere, Academic Press, 1988.

[002] [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. | Zbl 0799.30001

[003] [4] M. Berger, Géométrie 2, Cedic/Nathan, 1977.

[004] [5] F. M. Dekking, Recurrent sets, Adv. Math. 44 (1982), 78-104.

[005] [6] W. J. Gilbert, Complex numbers with three radix expansions, Canad. J. Math. 34 (1982), 1335-1348. | Zbl 0478.10007

[006] [7] W. J. Gilbert, Fractal geometry derived from complex bases, Math. Intelligencer 4 (1982), 78-86. | Zbl 0493.10010

[007] [8] W. J. Gilbert, Fractal dimension of sets derived from complex bases, Canad. Math. Bull. 29 (1986), 495-500. | Zbl 0564.10007

[008] [9] J. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 5 (1981), 713-747. | Zbl 0598.28011

[009] [10] S. Ito and M. Kimura, On the Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991), 461-486. | Zbl 0734.28010

[010] [11] S. Ito and M. Mizutani, Potato exchange transformations with fractal domains, preprint.

[011] [12] J. Kátai and J. Szabó, Canonical number systems for complex integers, Acta Sci. Math. (Szeged) 37 (1975), 255-260. | Zbl 0297.12003

[012] [13] D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, Addison-Wesley, Reading, MA, 1981. | Zbl 0477.65002

[013] [14] O. Lehto, Univalent Functions and Teichmüller Spaces, Springer, 1986.

[014] [15] A. Messaoudi, Autour du fractal de Rauzy, Thèse de l'Université de la Méditérannée, Aix-Marseille II, 1996.

[015] [16] A. Messaoudi, Propriétés arithmétiques et dynamiques du fractal de Rauzy, J. Théor. Nombres Bordeaux 10 (1998), 135-162. | Zbl 0918.11048

[016] [17] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. | Zbl 0522.10032

[017] [18] G. Rote, Sequences with subword complexity 2n, J. Number Theory 46 (1972), 196-213. | Zbl 0804.11023

[018] [19] V. Sirvent, Properties of geometrical realisations of substitutions associated to a family of Pisot numbers, Ph.D. thesis, Univ. of Warwick, 1993.

[019] [20] W. P. Thurston, Groups, tilings, and finite state automata, AMS Colloquium lectures, 1990.