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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Coding nested mixing one-sided subshifts
of finite type as Markov shifts having
exactly the same alphabet


Authors: Alejandro Maass and Servet Martínez
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BFK] M. Boyle, J. Franks, B. Kitchens, Automorphisms of one-sided subshifts of finite type, Ergodic Theory and Dynamical Systems 10, 421-449 (1990). MR 91h:58037
  • [BK] M. Boyle, W. Krieger, Automorphisms and subsystems of the shift, Journal für die reine und angewandte Mathematik 437, 13-28 (1993). MR 95b:54051
  • [LM] D. Lind, B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, (1995). MR 97a:58050
  • [Wi] R.F. Williams, Classification of subshifts of finite type, Ann. of Math. 98, 120-153 (1973); erratum Vol. 99, 380-381 (1974). MR 48:9769

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Additional Information

Alejandro Maass
Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
Email: amaass@dim.uchile.cl

Servet Martínez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
Email: smartine@dim.uchile.cl

DOI: https://doi.org/10.1090/S0002-9939-98-04174-4
Received by editor(s): April 16, 1996
Received by editor(s) in revised form: September 23, 1996
Communicated by: Mary Rees
Article copyright: © Copyright 1998 American Mathematical Society

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