Invariant densities for random $\beta$-expansions

K. Dajani, M. de Vries

Let $\beta >1$ be a non-integer. We consider expansions of the form ${\sum }_{i=1}^{\infty }{d}_i{\beta }^{-i}$, where the digits $(d_i{)}_{i\ge 1}$ are generated by means of a Borel map $K_{\beta }$ def…