I have been reading some papers recently, in particular, Blanchard's paper *$\beta$-expansions and symbolic dynamics* which state that a $\beta$-shift $S_{\beta}$ is a synchronised shift if and only if the orbit of the greedy $\beta$-expansion of $1$ is not dense in $S_{\beta}$.

The reference given for this result is a preprint due to A. Bertrand-Mathis, *Questions diverses relatives aux systemes codes: applications au $\beta$-shift*. Do you know any published reference where the proof can be found? Or, do you know a place where the preprint can be downloaded? 

I believe that the proof of this fact is similar to the proof for the fact that $S$-gap shifts are synchronised. If $\beta \in (1,2)$, must work in the same way. However, I am not sure if a similar argument will holds for $\beta > 2$.

Thanks in advance.