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Decompositions of factor codes and embeddings between shift spaces with unequal entropies

Published online by Cambridge University Press:  20 November 2012

SOONJO HONG ,
UIJIN JUNG  and
IN-JE LEE
SOONJO HONG
Affiliation:
Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de Chile, Chile (email: hsoonjo@dim.uchile.cl)
UIJIN JUNG
Affiliation:
Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de Chile, Chile (email: hsoonjo@dim.uchile.cl) School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, South Korea (email: uijin@kias.re.kr)
IN-JE LEE*
Affiliation:
306-1 Bolli-dong, Dalseo-gu, Daegu 704-913, South Korea (email: ijlee@kaist.ac.kr)
*
Current address: The Jesuit Novitiate of St. Stanislaus in Korea, 1196-43 Gyeongsu-daero, Jangan-gu, Suwon-si, Gyeonggi-do, South Korea (e-mail: paulusisj@gmail.com)
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Abstract

Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval from the entropy of Y to that of X. Furthermore, if X is of finite type, we can choose those intermediate subshifts as shifts of finite type. In the second part of the paper, given an embedding from a shift space to an irreducible sofic shift, we characterize the set of the entropies of the intermediate subshifts arising from the decompositions of the given embedding into embeddings.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 1 , February 2013 , pp. 144 - 157
Copyright
Copyright © Cambridge University Press 2013

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