‎ON THE ENTROPY OF A HALF SYNCHRONIZING SPACE

Abstract

‎

‎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.