Beyond Half Synchronized Systems
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.
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