Boundedness of oriented walks generated by substitutions

Dekking, F. M., and Wen, Z.-Y.. "Boundedness of oriented walks generated by substitutions." Journal de théorie des nombres de Bordeaux 8.2 (1996): 377-386. <http://eudml.org/doc/247843>.

@article{Dekking1996,
abstract = {Let $x = x_0x_1 \dots $ be a fixed point of a substitution on the alphabet $\left\lbrace a,b \right\rbrace ,$ and let $U_a = \left( \begin\{array\}\{rr\}-1 & -1\\ 0 & 1 \end\{array\} \right)$ and $U_b = \left( \begin\{array\}\{rr\} 1 & 1\\ 0 & 1 \end\{array\} \right)$. We give a complete classification of the substitutions $\sigma : \left\lbrace a, b \right\rbrace ^\{\star \}$ according to whether the sequence of matrices $\left( U_\{x_0\} U_\{x_1\} \dots U_\{x_n\} \right)^\infty _\{n=0\}$ is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.},
author = {Dekking, F. M., Wen, Z.-Y.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {substitutions; self-similarity; walks; automata sequences; boundedness; oriented one-dimensional walks; transition matrices},
language = {eng},
number = {2},
pages = {377-386},
publisher = {Université Bordeaux I},
title = {Boundedness of oriented walks generated by substitutions},
url = {http://eudml.org/doc/247843},
volume = {8},
year = {1996},
}

TY - JOUR
AU - Dekking, F. M.
AU - Wen, Z.-Y.
TI - Boundedness of oriented walks generated by substitutions
JO - Journal de théorie des nombres de Bordeaux
PY - 1996
PB - Université Bordeaux I
VL - 8
IS - 2
SP - 377
EP - 386
AB - Let $x = x_0x_1 \dots $ be a fixed point of a substitution on the alphabet $\left\lbrace a,b \right\rbrace ,$ and let $U_a = \left( \begin{array}{rr}-1 & -1\\ 0 & 1 \end{array} \right)$ and $U_b = \left( \begin{array}{rr} 1 & 1\\ 0 & 1 \end{array} \right)$. We give a complete classification of the substitutions $\sigma : \left\lbrace a, b \right\rbrace ^{\star }$ according to whether the sequence of matrices $\left( U_{x_0} U_{x_1} \dots U_{x_n} \right)^\infty _{n=0}$ is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.
LA - eng
KW - substitutions; self-similarity; walks; automata sequences; boundedness; oriented one-dimensional walks; transition matrices
UR - http://eudml.org/doc/247843
ER -