Two bifurcation sets arising from the beta transformation with a hole at $0$

Simon Baker, Derong Kong

Given $\beta \in (1,2],$ the $\beta$-transformation $T_{\beta }:x\mapsto \beta x(\mathrm{mod}1)$ on the circle $[0,1)$ with a hole $[0,t)$ was investigated by Kalle et al.~(2019). They described the set-valu…