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Infinite minimal half synchronizing | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 105-113 اصل مقاله (518.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19511.1266 | ||
| نویسنده | ||
| Manouchehr Shahamat* | ||
| Department of Mathematics, Dezful branch, Islamic Azad University, Dezful, Iran | ||
| چکیده | ||
| Synchronized systems, has attracted much attention in 1986 by F. Blanchard and G. Hansel, and extension of them has been of interest since that notion was introduced in 1992 by D. Fiebig and U. Fiebig. One was via half synchronized systems; that is, systems having half synchronizing blocks. In fact, if for a left transitive ray such as $\ldots x_{-1}x_{0}m$ and $mv$ any block in $X$ one has again $\ldots x_{-1}x_{0}mv$ a left ray in $X$, then $m$ is called half synchronizing. A block $m$ is minimal (half-)synchronizing, whenever $w \varsubsetneq m$, $w$ is not (half-)synchronizing. Examples with $\ell$ minimal (half-)synchronizing blocks has been given for $0\leq \ell\leq \infty$. To do this we consider a $\beta$-shift and will replace 1 with some blocks $u_i$ to have countable many new systems. Then, we will merge them. | ||
| کلیدواژه‌ها | ||
| minimal half synchronizing؛ synchronizing؛ entropy | ||
| مراجع | ||
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[1] D. Ahmadi Dastjerdi and M. Shahamat, Balanced Shifts, Communications in Mathematics and Applications Science, 11 (2020), 415-424.
[2] F. Blanchard and G. Hansel, Syst`emes cod´es, Comp. Sci. 44 (1986), 17-49.
[3] D. Fiebig and U. Fiebig, Covers for coded systems, Contemporary Mathematics, 135, 1992, 139-179.
[4] K. Johnson, Beta-shift dynamical systems and their associated languages, PhD Thesis, The University of North Carolina at Chapel Hill, 1999.
[5] D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ. Press. 1995.
[6] M. Shahamat, synchronized components of a subshift, J. Korean Math. Soc. 59 (2022), No. 1, pp. 1{12.
[7] K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys.356 (2006) 1235-1256.
[8] K. Thomsen, On the structure of a so c shift space, American Mathematical Society,356, Number 9 (2004), 3557-3619. | ||
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