[Substitutions inversibles et isomorphismes locaux]
Soient ϕ1 et ϕ2 deux substitutions primitives inversibles sur un alphabet de deux lettres. Soit ξϕ1 (resp. ξϕ2) un point fixe de ϕ1 (resp. ϕ2). Nous montrons que ξϕ1 et ξϕ2 sont localement isomorphes si et seulement s'il existe une substitution primitive inversible ϕ0 et deux entiers positifs m et n tels que Mϕ1=Mϕ0m et Mϕ2=Mϕ0n, où Mϕ est la matrice de la substitution ϕ.
Let ϕ1 and ϕ2 be two primitive invertible substitutions over a two-letter alphabet. Let ξϕ1 and ξϕ2 be fixed points of ϕ1 and ϕ2, respectively. We show that ξϕ1 and ξϕ2 are locally isomorphic if and only if there exists a primitive invertible substitution ϕ0 and two positive integers m and n such that Mϕ1=Mϕ0m and Mϕ2=Mϕ0n, where Mϕ is the substitutive matrix of the substitution ϕ.
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@article{CRMATH_2002__334_8_629_0,
author = {Wen, Zhi-Xiong and Wen, Zhi-Ying and Wu, Jun},
title = {Invertible substitutions and local isomorphisms},
journal = {Comptes Rendus. Math\'ematique},
pages = {629--634},
publisher = {Elsevier},
volume = {334},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02234-3},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02234-3/}
}
TY - JOUR AU - Wen, Zhi-Xiong AU - Wen, Zhi-Ying AU - Wu, Jun TI - Invertible substitutions and local isomorphisms JO - Comptes Rendus. Mathématique PY - 2002 SP - 629 EP - 634 VL - 334 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02234-3/ DO - 10.1016/S1631-073X(02)02234-3 LA - en ID - CRMATH_2002__334_8_629_0 ER -
%0 Journal Article %A Wen, Zhi-Xiong %A Wen, Zhi-Ying %A Wu, Jun %T Invertible substitutions and local isomorphisms %J Comptes Rendus. Mathématique %D 2002 %P 629-634 %V 334 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02234-3/ %R 10.1016/S1631-073X(02)02234-3 %G en %F CRMATH_2002__334_8_629_0
Wen, Zhi-Xiong; Wen, Zhi-Ying; Wu, Jun. Invertible substitutions and local isomorphisms. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 629-634. doi : 10.1016/S1631-073X(02)02234-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)02234-3/
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