Multiple expansions of real numbers with digits set $\{0,1,q\}$

Karma Dajani, Kan Jiang, Derong Kong +1

For $q>1$ we consider expansions in base $q$ over the alphabet $\{0,1,q\}$. Let ${\mathcal{U}}_q$ be the set of $x$ which have a unique $q$-expansions. For $k=2,3,\cdots ,{\aleph }_0$ l…