On the Entropy of a Half Synchronizing Space
DOI:
https://doi.org/10.22105/kmisj.v1i1.50Abstract
Thomsen in [K. Thomsen, on the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 356 (2006) 1235-1256] considers a synchronized component of a general subshift and investigates the approximation of entropy from inside of this synchronized component by some certain SFT's. A version of this theorem for half synchronized subshifts has been given. We continue by defining half synchronized entropy and the situation where it is equal to the topological entropy of the system. We consider them and in particular, a natural extension of the concept of synchronized entropy will be given for half synchronized systems denoted by $h_{hsyn}$ and we will show that if $h(X)=h_{hsyn}(X)$,
then $X$ is almost sofic.
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