Diophantine approximation of the orbit of 1 in the dynamical system of bete expansions

Bing Li, Tomas Persson, Baowei Wang +1

We consider the distribution of the orbits of the number 1 under the $\beta$-transformations $T_{\beta }$ as $\beta$ varies. Mainly, the size of the set of $\beta >1$ for which a given point can be we…