Schmidt's game, fractals, and numbers normal to no base

Ryan Broderick, Yann Bugeaud, Lior Fishman +2

Given $b>1$ and $y\in \mathbb{R}/\mathbb{Z}$, we consider the set of $x\in \mathbb{R}$ such that $y$ is not a limit point of the sequence $\{b^{n}x\mathrm{mod}1:n\in \mathbb{N}\}$. Su…