대한수학회지 (Journal of the Korean Mathematical Society)

  • 제59권1호
  • /
  • Pages.1-12
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  • 2022
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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SYNCHRONIZED COMPONENTS OF A SUBSHIFT

  • 투고 : 2020.03.02
  • 심사 : 2021.10.14
  • 발행 : 2022.01.01
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초록

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 [6]. Also, the common synchronized components of a subshift and its derived set have been characterized.

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참고문헌

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  2. D. Fiebig and U.-R. Fiebig, Covers for coded systems, in Symbolic dynamics and its applications (New Haven, CT, 1991), 139-179, Contemp. Math., 135, Amer. Math. Soc., Providence, RI, 1992. https://doi.org/10.1090/conm/135/1185086
  3. U. Jung, On the existence of open and bi-continuing codes, Trans. Amer. Math. Soc. 363 (2011), no. 3, 1399-1417. https://doi.org/10.1090/S0002-9947-2010-05035-4
  4. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995. https://doi.org/10.1017/CBO9780511626302
  5. K. Thomsen, On the structure of a sofic shift space, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3557-3619. https://doi.org/10.1090/S0002-9947-04-03437-3
  6. K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 26 (2006), no. 4, 1235-1256. https://doi.org/10.1017/S0143385706000290