Beyond Half Synchronized Systems

  • Dawoud Ahmadi Dastjerdi University of Guilan, Faculty of Mathematical Science, Rasht, Iran
  • Manouchehr Shahamat University of Guilan, Faculty of Mathematical Science, Rasht, Iran
Keywords: entropy, Fischer cover, Kreiger graph, half synchronized

Abstract

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 sofc shift space, American Mathematical Society, 356, Number 9, p. 557-3619] considers a synchronized component of a  general subshift and investigates the approximation of entropy from inside of this component by some certain SFT’s. We, using a rather different approach, show how this result extends to weak synchronized systems.

References

D. Fiebig and U. Fiebig, Covers for coded systems, Contemporary Mathematics, 135, 1992, 139-179.

U. Jung, On the existence of open and bi-continuous codes, Trans. Amer. Math. Soc. 363 (2011), 1399-1417.

D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ. Press. 1995.

T. Meyerovitvh, Tail invariant measures of the Dyke-shift and non-sofc systems, M.Sc. Thesis, Tel-Aviv university, 2004.

K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 356 (2006) 1235-1256.

K. Thomsen, On the structure of a sofc shift space, American Mathematical Society, 356, Number 9, 3557-3619

Published
2019-04-02
How to Cite
Ahmadi Dastjerdi, D., & Shahamat, M. (2019). Beyond Half Synchronized Systems. Majlesi Journal of Telecommunication Devices, 8(1). Retrieved from http://journals.iaumajlesi.ac.ir/td/index/index.php/td/article/view/526
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Articles