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Subshifts of multi-dimensional shifts of finite type

Published online by Cambridge University Press:  01 June 2000

ANTHONY N. QUAS  and
PAUL B. TROW
ANTHONY N. QUAS
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (e-mail: {quasa,trowp}@msci.memphis.edu)
PAUL B. TROW
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (e-mail: {quasa,trowp}@msci.memphis.edu)
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Abstract

We show that every shift of finite type $X$ with positive entropy has proper subshifts of finite type with entropy strictly smaller than the entropy of $X$, but with entropy arbitrarily close to the entropy of $X$. Consequently, $X$ contains an infinite chain of subshifts of finite type which is strictly decreasing in entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 3 , June 2000 , pp. 859 - 874
Copyright
2000 Cambridge University Press

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