Geometric realizations of substitutions

Bulletin de la Societe Mathematique de France

Volumn 126, Issue 2, 1998, Pages 149-179

  Holton, Charles ^a   Zamboni, Luca Q ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

Graph directed constructions; Limit sets; Substitutions

Indexed keywords

EID: 0000423217     PISSN: 00379484     EISSN: None     Source Type: Journal    
DOI: 10.24033/bsmf.2324     Document Type: Article

References (22)

1. ARNOUX (P.). - Représentation géométrique des systèmes dynamiques symboliques. - Habilitation à diriger des recherches, Université d'Aix-Marseille II, 1991.
2. BOMBIERI (E.), J.E. Taylor. - Quasicrystals, tilings, and algebraic number theory : Some preliminary connections, Contemp. Math., t. 64, 1987, p. 241-264.
3. BOSHERNITZAN (M.), I. Kornfeld. - Interval translation mappings, Ergod. Theor. & Dynam. Sys., t. 15, 1995, p. 821-832.
4. DEKKING (M.). - Recurrent sets, Adv. in Math., t. 44, 1982, p. 78-104.
5. DUMONT (J.M.). - Summation formulae for substitutions on a finite alphabet, Number Theory and Physics, J.M. Luck, P. Moussa, and M. Waldschmidt, eds., Proceedings in Physics #47, Springer Verlag, 1990.
6. FALCONER (K.J.). - The Geometry of Fractal Sets. - Cambridge University Press, New York, 1985.
7. FERENCZI (S.). - Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité 2n + 1, Bull. Soc. Math. France, 1995, p. 271-292.
8. GABORIAU (D.). - Dynamique des systèmes d'isométries : Sur les bouts des orbites, Invent. Math., t. 126, 1996, p. 297-318.
9. GABORIAU (D.)and G. Levitt. - The rank of actions on ℝ-trees, Ann. Sci. École Norm. Sup. (4), t. 28, 1995, p. 549-570.
10. HOLTON (C.), ZAMBONI (L.Q.). - Exotic actions on trees, Bull. London Math. Soc., t. 29, 1997, p. 309-313.
11. HOLTON (C.), ZAMBONI (L.Q.). - Substitutions, partial isometries of ℝ and actions on trees, Bull. Belgian Math. Soc. (in press).
12. HOLTON (C.), ZAMBONI (L.Q.). - Directed graphs and substitutions, preprint, 1997.
13. ITO (S.), KIMURA (M.). - On Rauzy fractal, Japan J. Indust. Appl. Math., t. 8, 1991, p. 461-486.
14. MARTIN (J.C.). - Minimal flows arising from substitutions of nonconstant length, Math. Syst. Th., t. 7, 1973, p. 73-82.
15. MAULDIN (R.D.), WILLIAMS (S.C.). - Hausdorff dimension in graph directed constructions, Trans. of the Amer. Math. Soc., t. 309, 1988, p. 811-829.
16. MICHEL (P.). - Stricte ergodicité d'ensembles minimaux de substitutions, C.R. Acad. Sc. Paris, t. 278, 1974, p. 811-813.
17. MOSSÉ (B.). - Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theor. Comp. Sci., t. 99, 1992, p. 327-334.
18. QUEFFÉLEC (M.). - Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. # 1294, 1987.
19. RAUZY (G.). - Nombres algébriques et substitutions, Bull. Soc. Math. France, t. 110, 1982, p. 147-178.
20. o 21, Univ. Bordeaux, Talence, 1987-1988.
21. SOLOMYAK (B.). - Substitutions, adic transformations and beta-expansions, Contemp. Math., t. 135, 1992, p. 361-372.
22. WALTERS (P.). - An Introduction to Ergodic Theory. - Springer-Verlag, New York, 1982.