Critical values for the ${\hat{I}}^2$-transformation with a hole at $0$

Pieter Allaart, Derong Kong

Given ${\hat{I}}^2\in (1,2]$, let $T_{\hat{I}}^2$ be the ${\hat{I}}^2$-transformation on the unit circle $[0,1)$ such that $T_{\hat{I}}^2(x)={\hat{I}}^{2}x(\mathrm{mod}1)$. For each $t\in [0,1)$ let $K_{\hat{I}}^2(t)$ be the survivor set consisti…