Matching for generalised $\beta$-transformations

Henk Bruin, Carlo Carminati, Charlene Kalle

We investigate matching for the family $T_{\alpha }(x)=\beta x+\alpha (\mathrm{mod}1)$, $\alpha \in [0,1]$, for fixed $\beta >1$. Matching refers to the property that there is an $n\in \mathbb{N}$ such that $T_α^n…