Identifications and dimension of the Rauzy fractal

Fractals

Volumn 5, Issue 2, 1997, Pages 281-294

  Sirvent, Víctor F ^a  

^a UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2742545382     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X97000279     Document Type: Article

References (13)

1. P. Arnoux, Un exemple de semi-conjugaison entre un échange d'intervalles et une rotation sur le tore, Bull. Soc. Math. France 116, 489-500 (1988).
2. P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n + 1, Bull Soc. Math. France 119, 199-215 (1991).
3. L. Carleson, Selected Problems on Exceptional Sets (Van Nostrand, Princeton, 1967).
4. K. Falconer, Fractal Geometry - Mathematical Foundations and Applications (John Wiley & Sons, Chichester, 1990).
5. F. R. Gantmacher, Matrix Theory, Vol. 2 (Chelsea, New York, 1959).
6. S. Ito, Weyl automorphisms, substitutions and fractals in Stability Theory and Related Topics in Dynamical Systems (Nagoya, 1988), pp. 60-72, World Sci. Adv. Ser. Dyn. Syst., Vol. 6 (World Sci. Publishing, Teaneck, NJ, 1989).
7. S. Ito and M. Kimura, "On the Rauzy fractal," Japan J. Indust. Appl. Math. 8, 461-486 (1991).
8. M. Queffelec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Mathematics, Vol. 1294 (Springer-Verlag, Berlin, 1987).
9. G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110, 147-178 (1982).
10. V. F. Sirvent, Properties of Geometrical Realizations of Substitutions associated to a Family of Pisot Numbers, Ph.D. thesis (University of Warwick, 1993).
11. V. F. Sirvent, Geodesic laminations as geometric realizations of Pisot substitutions. Preprint.
12. V. F. Sirvent, The Arnoux semi-conjugacy is Hölder continuous. Preprint.
13. V. F. Sirvent, "Relationships between the dynamical systems associated to the Rauzy substitutions," Theor. Comp. Sci. 164, 41-57 (1996).