Beyond half synchronized systems
محورهای موضوعی : Majlesi Journal of Telecommunication DevicesDawoud Ahmadi Dastjerdi 1 , Manouchehr Shahamat 2
1 - University of Guilan, Faculty of Mathematical Science, Rasht, Iran
2 -
کلید واژه: Fischer cover, Entropy, half synchronized, Kreiger graph,
چکیده مقاله :
In irreducible subshifts, a word m is synchronizing if whenever vm and mw are admissible words, then vmw is admissible as well. A word m is (left) half (resp. weak) synchronizing, when there is a left transitive ray (resp. a left ray) x− such that if x−m and mw are admissible, then x−mw is also admissible. The respective subshifts are called half (resp. weak) synchronized. K. Thomsen in [On the structure of a sofic shift space, American Mathematical Society, 356, Number 9, 3557-3619] considers a synchronized component of a general subshift and investigates the approximation of entropy from inside of this component by some certain SFTs. We, using a rather different approach, show how this result extends to weak synchronized systems.
[1] D. Fiebig and U. Fiebig, Covers for coded systems, Contemporary Mathematics, 135, 1992, 139-179.
[2] U. Jung, On the existence of open and bi-continuous codes, Trans. Amer. Math. Soc. 363 (2011), 1399-1417.
[3] D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ. Press. 1995.
[4] T. Meyerovitvh, Tail invariant measures of the Dyke-shift and non-sofc systems, M.Sc. Thesis, Tel-Aviv university, 2004.
[5] K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 356 (2006) 1235-1256.
[6] K. Thomsen, On the structure of a sofc shift space, American Mathematical Society, 356, Number 9, 3557-3619
