Invertible substitutions and local isomorphisms

Zhi-Xiong Wen; Zhi-Ying Wen; Jun Wu

doi:10.1016/S1631-073X(02)02234-3

Invertible substitutions and local isomorphisms
[Substitutions inversibles et isomorphismes locaux]

Zhi-Xiong Wen ¹ ; Zhi-Ying Wen ² ; Jun Wu ¹

¹ Nonlinear Science Center, Department of Mathematics, Wuhan University, Wuhan 430072, China
² Department of Mathematics, Tsinghua University, Beijing 10084, China

Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 629-634.

Résumé
Abstract

Soient ϕ₁ et ϕ₂ deux substitutions primitives inversibles sur un alphabet de deux lettres. Soit ξ_ϕ₁ (resp. ξ_ϕ₂) un point fixe de ϕ₁ (resp. ϕ₂). Nous montrons que ξ_ϕ₁ et ξ_ϕ₂ sont localement isomorphes si et seulement s'il existe une substitution primitive inversible ϕ₀ et deux entiers positifs m et n tels que M_ϕ₁=M_ϕ₀^m et M_ϕ₂=M_ϕ₀ⁿ, où M_ϕ est la matrice de la substitution ϕ.

Let ϕ₁ and ϕ₂ be two primitive invertible substitutions over a two-letter alphabet. Let ξ_ϕ₁ and ξ_ϕ₂ be fixed points of ϕ₁ and ϕ₂, respectively. We show that ξ_ϕ₁ and ξ_ϕ₂ are locally isomorphic if and only if there exists a primitive invertible substitution ϕ₀ and two positive integers m and n such that M_ϕ₁=M_ϕ₀^m and M_ϕ₂=M_ϕ₀ⁿ, where M_ϕ is the substitutive matrix of the substitution ϕ.

Reçu le : 2001-10-24
Accepté le : 2001-12-03
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02234-3

Affiliations des auteurs :

Zhi-Xiong Wen ¹ ; Zhi-Ying Wen ² ; Jun Wu ¹

¹ Nonlinear Science Center, Department of Mathematics, Wuhan University, Wuhan 430072, China
² Department of Mathematics, Tsinghua University, Beijing 10084, China

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Zhi-Xiong Wen; Zhi-Ying Wen; Jun Wu. Invertible substitutions and local isomorphisms. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 629-634. doi : 10.1016/S1631-073X(02)02234-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02234-3/

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Cité par Sources :

^☆ Supported by the Special Funds for Major State Basic Research Projects of China and Morningside Center of Mathematics (CAS).

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