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Reversible topological Markov shifts

Published online by Cambridge University Press:  13 January 2006

JUNGSEOB LEE ,
KEYWON K. PARK  and
SUJIN SHIN
JUNGSEOB LEE
Affiliation:
Department of Mathematics, Ajou University, Suwon 443-749, Korea (e-mail: jslee@ajou.ac.kr, kkpark@ajou.ac.kr)
KEYWON K. PARK
Affiliation:
Department of Mathematics, Ajou University, Suwon 443-749, Korea (e-mail: jslee@ajou.ac.kr, kkpark@ajou.ac.kr)
SUJIN SHIN
Affiliation:
Department of Mathematics, KAIST, Daejeon 305-701, Korea (e-mail: sjs@math.kaist.ac.kr)
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Abstract

We generalize the notion of reversible systems in symbolic dynamics, and investigate their properties. It is shown that a reversible topological Markov shift can be represented by a pair of matrices of special types. This enables us to classify the invariant measures of the reversible systems. Necessary and/or sufficient conditions for the existence of a reversal of finite order are established in terms of the adjacency matrices. We also prove that a topological Markov shift with a reversal of order two admits reversals of all orders.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 1 , February 2006 , pp. 267 - 280
Copyright
2006 Cambridge University Press

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