Expansions in non-integer bases: lower order revisited

Simon Baker, Nikita Sidorov

Let $q\in (1,2)$ and $x\in [0,\frac{1}{q-1}]$. We say that a sequence $({\epsilon }_i{)}_{i=1}^{\infty }\in \{0,1{\}}^{\mathbb{N}}$ is an expansion of $x$ in base $q$ (or a $q$-expansion) if…