Let be a fixed point of a substitution on the alphabet and let and . We give a complete classification of the substitutions according to whether the sequence of matrices is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.
Soit un point fixe de la substitution sur l’alphabet et soit et . On donne une classification complète des substitutions selon que la suite de matrices est bornée ou non. Cela correspond au fait que les chemins orientés engendrés par les substitutions sont bornés ou non.
@article{JTNB_1996__8_2_377_0, author = {F. M. Dekking and Z.-Y. Wen}, title = {Boundedness of oriented walks generated by substitutions}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {377--386}, publisher = {Universit\'e Bordeaux I}, volume = {8}, number = {2}, year = {1996}, zbl = {0869.11020}, mrnumber = {1438476}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_377_0/} }
TY - JOUR AU - F. M. Dekking AU - Z.-Y. Wen TI - Boundedness of oriented walks generated by substitutions JO - Journal de théorie des nombres de Bordeaux PY - 1996 SP - 377 EP - 386 VL - 8 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_377_0/ LA - en ID - JTNB_1996__8_2_377_0 ER -
%0 Journal Article %A F. M. Dekking %A Z.-Y. Wen %T Boundedness of oriented walks generated by substitutions %J Journal de théorie des nombres de Bordeaux %D 1996 %P 377-386 %V 8 %N 2 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_377_0/ %G en %F JTNB_1996__8_2_377_0
F. M. Dekking; Z.-Y. Wen. Boundedness of oriented walks generated by substitutions. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 377-386. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_377_0/
[1] Recurrent sets, Advances in Math. 44 (1982), 78-104. | MR | Zbl
,[2] On transience and recurrence of generalized random walks, Z. Wahrsch. verw. Geb. 61 (1982), 459-465. | MR | Zbl
,[3] es automatiques, J. Théor. Nombres Bordeaux 5 (1993), 93-100. | Numdam | MR | Zbl
, March[4] Iteration of maps by an automaton, Discrete Math. 126 (1994), 81-86. | MR | Zbl
,[5] Systèmes de numération et fonctions fractales relatifs aux substitutions, Theor. Comp. Science 65 (1989), 153-169. | MR | Zbl
et ,[6] Summation formulae for substitutions on a finite alphabet, Number Theory and Physics (Eds: J.-M. Luck, P. Moussa, M. Waldschmidt). Springer Lect. Notes Physics 47 (1990), 185-194. | MR | Zbl
,[7] Wirebending and continued fractions, J. Combinatorial Theory Ser. A 50 (1989), 1-23. | MR | Zbl
and ,[8] Quasicrystals (I). Definition and structure. Physical Review B, vol. (2) 34, 1986, 596-615. | MR
and ,[9] Quasicrystallography: some interesting new patterns. Banach center publications, vol. 17, 1985, 439-461. | MR | Zbl
,[10] Marches sur les arbres homogènes suivant une suite substitutive, J. Théor. Nombres Bordeaux, 4 (1992), 155-186. | Numdam | MR | Zbl
and ,