Coding nested mixing one-sided subshifts of finite type as Markov shifts having exactly the same alphabet
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- by Alejandro Maass and Servet Martínez PDF
- Proc. Amer. Math. Soc. 126 (1998), 1219-1230 Request permission
Abstract:
Let $X_{0}$, $X$ be mixing one-sided subshifts of finite type such that $X_{0}\subseteq X$. We show a necessary and sufficient condition for the existence of mixing Markov shifts $Y_{0}$, $Y$, $Y_{0}\subseteq Y$, and a conjugacy $\pi : Y\to X$ with $\pi (Y_{0})=X_{0}$, such that the sets of letters appearing in both systems are the same, more precisely, $L_{1}(Y_{0})=L_{1}(Y)$.References
- Mike Boyle, John Franks, and Bruce Kitchens, Automorphisms of one-sided subshifts of finite type, Ergodic Theory Dynam. Systems 10 (1990), no. 3, 421–449. MR 1074312, DOI 10.1017/S0143385700005678
- Mike Boyle and Wolfgang Krieger, Automorphisms and subsystems of the shift, J. Reine Angew. Math. 437 (1993), 13–28. MR 1212251, DOI 10.1515/crll.1993.437.13
- Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995. MR 1369092, DOI 10.1017/CBO9780511626302
- R. F. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120–153; errata, ibid. (2) 99 (1974), 380–381. MR 331436, DOI 10.2307/1970908
Additional Information
- Alejandro Maass
- Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
- MR Author ID: 315077
- ORCID: 0000-0002-7038-4527
- Email: amaass@dim.uchile.cl
- Servet Martínez
- Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
- MR Author ID: 120575
- Email: smartine@dim.uchile.cl
- Received by editor(s): April 16, 1996
- Received by editor(s) in revised form: September 23, 1996
- Communicated by: Mary Rees
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1219-1230
- MSC (1991): Primary 54H20, 58F03
- DOI: https://doi.org/10.1090/S0002-9939-98-04174-4
- MathSciNet review: 1425133