Geodesic
On invertible substitutions with two fixed points
[Sur les substitutions inversibles ayant deux points fixes]
Wen, Zhi-Xiong1 ; Wen, Zhi-Ying2 ; Wu, Jun1
1 Nonlinear Science Center, Department of Mathematics, Wuhan University, Wuhan 430072, China
2 Department of Mathematics, Tsinghua University, Beijing 10084, China
Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 727-731

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Let ϕ be a primitive substitution on a two-letter alphabet {a,b} having two fixed points ξa and ξb. We show that the substitution ϕ is invertible if and only if one has ξa=abξ and ξb=baξ.

On considère une substitution primitive ϕ sur l'alphabet {a,b} ayant deux points fixes ξa et ξb (commençant respectivement par a et b). Nous montrons que la substitution ϕ est inversible si et seulement si l'on a ξa=abξ et ξb=baξ.

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Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02235-5

Wen, Zhi-Xiong 1 ; Wen, Zhi-Ying 2 ; Wu, Jun 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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Wen, Zhi-Xiong; Wen, Zhi-Ying; Wu, Jun. On invertible substitutions with two fixed points. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 727-731. doi: 10.1016/S1631-073X(02)02235-5

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