sturmian words are infinite words that have exactly factors of length for every positive integer . A sturmian word is also defined as a coding over a two-letter alphabet of the orbit of point under the action of the irrational rotation (mod 1). A substitution fixes a sturmian word if and only if it is invertible. The main object of the present paper is to investigate Rauzy fractals associated with two-letter invertible substitutions. As an application, we give an alternative geometric proof of Yasutomi’s characterization of all pairs such that is a fixed point of some non-trivial substitution.
Mots-clés : sturmian words, Rauzy fractals, invertible substitutions, automorphisms of the free monoid, tilings
@article{ITA_2007__41_3_329_0, author = {Berth\'e, Val\'erie and Ei, Hiromi and Ito, Shunji and Rao, Hui}, title = {On substitution invariant sturmian words : an application of {Rauzy} fractals}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {329--349}, publisher = {EDP-Sciences}, volume = {41}, number = {3}, year = {2007}, doi = {10.1051/ita:2007026}, mrnumber = {2354361}, zbl = {1140.11014}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2007026/} }
TY - JOUR AU - Berthé, Valérie AU - Ei, Hiromi AU - Ito, Shunji AU - Rao, Hui TI - On substitution invariant sturmian words : an application of Rauzy fractals JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2007 SP - 329 EP - 349 VL - 41 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2007026/ DO - 10.1051/ita:2007026 LA - en ID - ITA_2007__41_3_329_0 ER -
%0 Journal Article %A Berthé, Valérie %A Ei, Hiromi %A Ito, Shunji %A Rao, Hui %T On substitution invariant sturmian words : an application of Rauzy fractals %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 329-349 %V 41 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2007026/ %R 10.1051/ita:2007026 %G en %F ITA_2007__41_3_329_0
Berthé, Valérie; Ei, Hiromi; Ito, Shunji; Rao, Hui. On substitution invariant sturmian words : an application of Rauzy fractals. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 3, pp. 329-349. doi : 10.1051/ita:2007026. http://archive.numdam.org/articles/10.1051/ita:2007026/
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