Bifurcation sets arising from non-integer base expansions

Pieter Allaart, Simon Baker, Derong Kong

Given a positive integer $M$ and $q\in (1,M+1]$, let ${\mathcal{U}}_q$ be the set of $x\in [0,M/(q-1)]$ having a unique $q$-expansion: there exists a unique sequence $(x_i)=x_1x_2\ldot…