Hausdorff dimension of double base expansions and binary shifts with a hole

Jian Lu, Wolfgang Steiner, Yuru Zou

For two real bases $q_0,q_1>1$, a binary sequence $i_1{i}_2\cdots \in \{0,1{\}}^{\infty }$ is the $(q_0,q_1)$-expansion of the number \[ π_{q_0,q_1}(i_1 i_2 \cdots) = \sum_{k=1}^\in…