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Synchronized components of a subshift
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We introduce the notion of a minimal synchronizing word; that is a synchronizing word whose proper subwords are not synchronized. This has been used to give a new shorter proof for a theorem in \cite{Thomsen1}. Also, the common synchronized components of a subshift and its derived set have been characterized.
Abstract
We introduce the notion of a minimal synchronizing word; that is a synchronizing word whose proper subwords are not synchronized. This has been used to give a new shorter proof for a theorem in \cite{Thomsen1}. Also, the common synchronized components of a subshift and its derived set have been characterized.
참고문헌 (6)
- D. A. Dastjerdi, "Dynamics and topology of S-gap shifts", Topology Appl, 159(10-11), pp.2654~2661 (2012)[DOI]
- D. Fiebig, "Symbolic dynamics and its applications", pp.139~179 (1992), Amer. Math. Soc
- U. Jung, "On the existence of open and bi-continuing codes", Trans. Amer. Math. Soc, 363(3), pp.1399~1417 (2011)[DOI]
- D. Lind, "An Introduction to Symbolic Dynamics and Coding" (1995), Cambridge University Press
- K. Thomsen, "On the structure of a sofic shift space", Trans. Amer. Math. Soc, 356(9), pp.3557~3619 (2004)[DOI]
- K. Thomsen, "On the ergodic theory of synchronized systems", Ergod. Th. Dynam. Sys, 26(4), pp.1235~1256 (2006)[DOI]
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