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On the number of fixed points of a sofic shift-flip system

Published online by Cambridge University Press:  20 August 2013

YOUNG-ONE KIM  and
SIEYE RYU
YOUNG-ONE KIM
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email kimyo@math.snu.ac.krmandu0@snu.ac.kr
SIEYE RYU
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email kimyo@math.snu.ac.krmandu0@snu.ac.kr
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Abstract

If $X$ is a sofic shift and $\varphi : X\rightarrow X$ is a homeomorphism such that ${\varphi }^{2} = {\text{id} }_{X} $ and $\varphi {\sigma }_{X} = { \sigma }_{X}^{- 1} \varphi $, the number of points in $X$ that are fixed by ${ \sigma }_{X}^{m} $ and ${ \sigma }_{X}^{n} \varphi , m= 1, 2, \ldots , n\in \mathbb{Z} $, is expressed in terms of a finite number of square matrices: the matrices are obtained from Krieger’s joint state chain of a sofic shift which is conjugate to $X$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 2 , April 2015 , pp. 482 - 498
Copyright
© Cambridge University Press, 2013 

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