Boundedness of oriented walks generated by substitutions
Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, p. 377-386

Let x=x 0 x 1 be a fixed point of a substitution on the alphabet a,b, and let U a =-1-101 and U b =1101. We give a complete classification of the substitutions σ:a,b according to whether the sequence of matrices U x 0 U x 1 U x n n=0 is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

Soit x=x 0 x 1 un point fixe de la substitution sur l’alphabet a,b, et soit U a =-1-101 et U b =1101. On donne une classification complète des substitutions σ:a,b selon que la suite de matrices U x 0 U x 1 U x n n=0 est bornée ou non. Cela correspond au fait que les chemins orientés engendrés par les substitutions sont bornés ou non.

Keywords: substitutions, self-similarity, walks
@article{JTNB_1996__8_2_377_0,
     author = {Dekking, Michel and Wen, Zhi-Ying},
     title = {Boundedness of oriented walks generated by substitutions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
     pages = {377-386},
     zbl = {0869.11020},
     mrnumber = {1438476},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1996__8_2_377_0}
}
Dekking, F. M.; Wen, Z.-Y. Boundedness of oriented walks generated by substitutions. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 377-386. http://www.numdam.org/item/JTNB_1996__8_2_377_0/

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